Class 10 Science Notes Chapter 10 Wave

Introduction to Wave Phenomena in Chapter 10 Wave

The pencil partially dipped in water appears bent due to the difference in speed of light waves in air and water. This illustrates the basic principle of light behavior in different media.

Air bubbles shine in water because light reflects from their surface, based on the same principle as optical fiber, where light is trapped and guided through total internal reflection.

A hand lens enlarges letters due to its curved structure, which bends light rays to form magnified images.

A rainbow forms when sunlight splits into seven colors through dispersion in water droplets. Cone cells in our eyes enable us to perceive these colors, making the rainbow visible.

Vision can blur if the eye lens fails to adjust thickness or loses transparency. Issues like difficulty seeing distant or nearby objects, or distinguishing colors, are corrected with spectacles having appropriate lens power.

Light speed varies across media, classifying them as rarer media (higher speed) or denser media (lower speed). This classification is crucial for understanding refraction and reflection phenomena in Chapter 10 Wave.

Denser and Rarer Medium in Chapter 10 Wave

The speed of light in various media is as follows:

Medium	Speed (m/s)
Air	3.00 × 10⁸
Water	2.25 × 10⁸
Glass	2.00 × 10⁸
Diamond	1.24 × 10⁸

For example, glass is denser than air because light slows down more in glass. Optical density differs from physical density; kerosene is optically denser than water but physically less dense, as it floats on water.

Refraction of Light in Chapter 10 Wave

When light moves from a rarer medium (like air) to a denser medium (like water), it bends towards the normal. Conversely, from denser to rarer, it bends away from the normal.

The extent of bending depends on the change in speed: greater change means more refraction. This principle applies not only to light but also to other waves like sound.

Laws of Refraction of Light in Chapter 10 Wave

1. The incident ray, refracted ray, and normal at the point of incidence all lie in the same plane.

2. The ratio of the sine of the angle of incidence (\(\sin i\)) to the sine of the angle of refraction (\(\sin r\)) is constant for a given pair of media: \(\frac{\sin i}{\sin r} = \mu\) (refractive index).

Refractive index \(\mu = \frac{c}{v}\), where c is speed in vacuum/air, v in medium.

Medium	Refractive Index	Speed (m/s)
Water	1.33	2.25 × 10⁸
Glass	1.50	2.00 × 10⁸
Diamond	2.42	1.24 × 10⁸

Higher refractive index indicates slower light speed in the medium, essential for understanding optical phenomena in Chapter 10 Wave.

Consequences of Refraction of Light in Chapter 10 Wave

A coin in water appears raised because light rays bend away from the normal at the water-air interface, forming an image at a shallower apparent depth.

Objects partially dipped in water appear bent, and water depths seem less than actual due to refraction.

Stars twinkle from atmospheric refraction through varying density layers, causing light to bend randomly.

The sun is visible 2 minutes before actual sunrise and after sunset due to atmospheric bending of light rays.

Total Internal Reflection of Light in Chapter 10 Wave

Conditions for TIR:

1. Light travels from denser to rarer medium.

2. Angle of incidence exceeds critical angle.

All light is reflected, no loss, unlike regular reflection.

Critical Angle in Chapter 10 Wave

Medium	Critical Angle
Water	49°
Glass	42°
Diamond	24°

Value depends on media pair and refractive indices.

Consequences of Total Internal Reflection of Light in Chapter 10 Wave

Diamond sparkles from high refractive index (2.42), small critical angle (24°), multiple TIR in facets.

Surfaces shine like air bubbles in water or empty tube due to TIR at interfaces.

Mirage: TIR in hot air layers creates inverted images appearing as water pools.

Optical Fibre in Chapter 10 Wave

Structure: Core (higher n), cladding (lower n) for TIR.

Uses in telecommunication: High-speed data transmission (1 Gbps).

Medical uses: Endoscopy (view digestive system), colonoscopy (examine colon), keyhole surgery (minimally invasive operations).

Dispersion of Light in Chapter 10 Wave

Visible spectrum: VIBGYOR, violet bends most, red least.

Reason: Refractive index varies with wavelength; shorter wavelengths (violet) slow more, bend more.

Newton’s disc: Spins to mix colors into white.

Rainbow in Chapter 10 Wave

Process: Light refracts into drop, disperses, TIR inside, refracts out.

Semicircular due to fixed angles (red 42°, violet 40°).

Lens in Chapter 10 Wave

Convex Lens: Converges rays, thicker in middle, positive f.

Concave Lens: Diverges rays, thinner in middle, negative f.

Terminologies Related to a Lens in Chapter 10 Wave

Focal Length in Chapter 10 Wave

Rules to Draw Image Formed by a Convex Lens in Chapter 10 Wave

1. Rays through optical center pass straight.

2. Parallel rays converge through focus (convex) or appear from focus (concave).

3. Rays through focus emerge parallel.

The Image Formed by a Convex Lens in Chapter 10 Wave

Object Position	Image Position	Characteristics	Use
At infinity	At F	Real, inverted, highly diminished	Telescope objective
Beyond 2F	Between F and 2F	Real, inverted, diminished	Camera
At 2F	At 2F	Real, inverted, same size	Terrestrial telescope
Between F and 2F	Beyond 2F	Real, inverted, magnified	Projector
At F	At infinity	Real, inverted, highly magnified	Flashlight
Between F and O	Same side	Virtual, erect, magnified	Hand lens

Image size increases as object nears lens.

Image Formed by a Concave Lens in Chapter 10 Wave

Always virtual, erect, diminished, regardless of object position. Used in door peepholes for wide view.

Power of a Lens in Chapter 10 Wave

Formula: \( P = \frac{1}{f} \) (f in m).

Higher power means shorter f, stronger bending.

Human Eye in Chapter 10 Wave

Cornea: Transparent front layer, main refractor (2/3 power).

Pupil: Opening for light, size controlled by iris.

Iris: Colored muscle adjusting pupil for light control.

Lens: Flexible, focuses light on retina.

Ciliary Muscles: Adjust lens curvature for focusing.

Retina: Light-sensitive screen with rods (brightness, low light) and cones (color).

Optic Nerve: Transmits signals to brain.

Brain inverts retina’s upside-down image.

Accommodation of Eye in Chapter 10 Wave

For distant objects: Ciliary muscles relax, lens thins, longer f.

For near objects: Muscles contract, lens thickens, shorter f.

Far Point and Near Point of the Human Eye in Chapter 10 Wave

Normal vision range: 25 cm to infinity.

Defects of Vision in Chapter 10 Wave

Myopia (Shortsightedness): Distant objects blurry, image in front of retina. Causes: Elongated eyeball, excessive lens curvature. Correction: Concave lens diverges rays.

Hypermetropia (Longsightedness): Near objects blurry, image behind retina. Causes: Short eyeball, insufficient lens curvature. Correction: Convex lens converges rays.

Other Ways for Correction of Defect of Vision in Chapter 10 Wave

Advantages: Full field, no distortion; disadvantages: Hygiene needed, risk of infection.

LASIK: Flap created, stroma reshaped, flap replaced.

Other Problems Related to the Eye in Chapter 10 Wave

Dr. Sanduk Ruit developed affordable IOL for cataract treatment.

Effects of Injuries to the Cornea in Chapter 10 Wave

Cornea injuries from dust, rubbing cause scratches, blurred vision.

Infections lead to ulcers (keratitis), edema, keratoconus (conical shape).

Treatment: Medication or transplantation if severe.

Corneal Transplantation in Chapter 10 Wave

Donated corneas stored in eye banks like Nepal Eye Bank.

For congenital issues, infections, injuries.

A. Choose the correct option for the following questions.

2. Differentiate between

(a) Reflection of Light and Total Internal Reflection of Light

Feature	Reflection of Light	Total Internal Reflection of Light
Medium Condition	Can occur when light hits any surface (e.g., from air to mirror).	Occurs only when light travels from a denser medium to a rarer medium.
Angle Condition	Occurs at any angle of incidence.	Occurs only when the angle of incidence is greater than the critical angle.
Refraction	Refraction may occur simultaneously if the surface is transparent.	No refraction occurs; the ray does not enter the second medium.
Energy Loss	Some light energy is absorbed by the reflecting surface, so reflection is partial.	100% of the light is reflected. There is no loss of light energy.
Image Brightness	The image formed is less bright than the object.	The image formed is as bright as the object.

(b) Concave Lens and Convex Lens

Feature	Concave Lens	Convex Lens
Shape	Thinner at the center and thicker at the edges.	Thicker at the center and thinner at the edges.
Action on Light	Diverges parallel rays of light. Also known as a diverging lens.	Converges parallel rays of light. Also known as a converging lens.
Focal Point	Has a virtual focal point (rays appear to diverge from it).	Has a real focal point (rays actually meet at it).
Focal Length	Focal length is considered negative by sign convention.	Focal length is considered positive by sign convention.
Image Formation	Always forms a virtual, erect, and diminished image.	Can form real, inverted, or virtual, erect images of various sizes.
Primary Use	Used to correct short-sightedness (myopia).	Used to correct long-sightedness (hypermetropia) and as a magnifying glass.

(c) Near Point and Far Point of the Eye

Feature	Near Point (Punctum Proximun)	Far Point (Punctum Remotum)
Definition	The closest distance at which an object can be seen clearly without strain.	The farthest distance at which an object can be seen clearly without strain.
Normal Value	For a normal adult eye, it is about 25 cm.	For a normal eye, it is at infinity.
Muscle State	The ciliary muscles are fully contracted to make the lens thick.	The ciliary muscles are completely relaxed, and the lens is at its thinnest.
Effect of Age	Increases with age (a condition known as presbyopia).	Remains at infinity for a normal eye but is closer for a myopic eye.
Vision Defect	A near point greater than 25 cm is a symptom of long-sightedness.	A finite far point (closer than infinity) is a symptom of short-sightedness.

(d) Short-sightedness and Long-sightedness

Feature	Short-sightedness (Myopia)	Long-sightedness (Hypermetropia)
Symptom	A person can see nearby objects clearly but distant objects appear blurry.	A person can see distant objects clearly but nearby objects appear blurry.
Cause	The eyeball is too long, or the eye lens is too converging (short focal length).	The eyeball is too short, or the eye lens is not converging enough (long focal length).
Image Focus	The image of a distant object is formed in front of the retina.	The image of a nearby object is formed behind the retina.
Far Point	The far point is closer than infinity.	The near point is farther than 25 cm.
Corrective Lens	Corrected using a concave (diverging) lens.	Corrected using a convex (converging) lens.

(e) Color Blindness and Night Blindness

Feature	Color Blindness	Night Blindness (Nyctalopia)
Cause	A genetic condition where cone cells in the retina are absent or do not function correctly.	Often caused by a deficiency of Vitamin A, which affects the function of rod cells.
Affected Cells	Cone cells, which are responsible for color vision.	Rod cells, which are responsible for vision in low light (scotopic vision).
Symptom	Inability or decreased ability to see color or perceive differences between colors.	Difficulty or inability to see in relatively low light or at night.
Vision in Light	Vision in bright light is generally normal, apart from color perception.	Vision in bright light is typically unaffected.
Treatment	There is no cure, but special lenses can help in distinguishing some colors.	Can often be treated by addressing the underlying cause, e.g., Vitamin A supplements.

3. Give reasons:

(a) Between glass and water, glass is considered a denser medium and water is a rarer medium.

Reason: Optical density is determined by how much a medium slows down the speed of light. Light travels slower in glass (approx. 2 x 10⁸ m/s) than in water (approx. 2.25 x 10⁸ m/s). Because light is slower in glass, glass has a higher refractive index and is considered optically denser than water.

(b) When a coin is placed in a glass containing water, it appears to rise a bit.

Reason: This phenomenon is due to the refraction of light. Light rays traveling from the coin (in the denser water medium) bend away from the normal as they exit into the air (the rarer medium) before reaching our eyes. Our brain interprets these bent rays as coming in a straight line from a shallower position. This makes the coin appear to be at a raised, or “apparent,” depth, which is less than its real depth.

(c) When the letters written on paper are observed from the top of a glass slab, the letters appear to be slightly raised.

Reason: This is the same principle as the coin in water. Light rays from the letters travel from the paper, through the denser glass slab, and into the rarer air medium to reach the observer’s eye. As the rays exit the glass, they bend away from the normal. This makes the letters appear to be at a shallower depth than they actually are, causing them to look raised.

(d) Stars twinkle.

Reason: The twinkling of stars is caused by atmospheric refraction. Starlight travels through many layers of the Earth’s atmosphere, which have different temperatures and densities. These layers are constantly moving. As the light from a distant star (a point source) passes through these turbulent layers, it is refracted multiple times in random directions. This causes the apparent position and brightness of the star to fluctuate, which we perceive as twinkling.

(e) The sun appears on the horizon about two minutes before the actual sunrise.

Reason: This is an effect of atmospheric refraction. When the sun is slightly below the horizon, its light rays travel from the vacuum of space (rarer) into the Earth’s atmosphere (denser). The atmosphere bends the sunlight downwards. To an observer on Earth, this bending makes the sun appear to be above the horizon when it is still physically below it. This effect accounts for an apparent sunrise about two minutes early and a delayed sunset of about two minutes.

(f) A diamond appears to shine but a piece of glass cut to the same shape does not shine.

Reason: A diamond shines brilliantly due to total internal reflection (TIR). Diamond has a very high refractive index (about 2.42), which results in a very small critical angle (about 24°). It is cut with many facets at specific angles so that most of the light entering it strikes an internal surface at an angle greater than the critical angle. This causes the light to be totally internally reflected multiple times before exiting, creating the characteristic sparkle. Glass has a lower refractive index (~1.5) and a larger critical angle (~42°), so less light undergoes TIR, and it appears less brilliant.

(g) Sunlight is refracted when it is passed through a prism.

Reason: Sunlight is refracted because it undergoes a change in speed as it moves from one medium (air) to another (the glass of the prism). When the light ray enters the prism at an angle, this change in speed causes it to bend. It bends again when it exits the prism, moving from glass back to air. This double bending is characteristic of refraction through a prism.

(h) A convex lens converges light rays.

Reason: A convex lens is thicker in the middle. Parallel rays of light entering the lens are refracted at both surfaces. Due to the curved shape of the surfaces, each ray is bent inwards towards the principal axis. All the rays meet at a single point on the principal axis called the principal focus. Because it brings rays together, it is called a converging lens.

(i) A concave lens diverges the rays of light.

Reason: A concave lens is thinner in the middle. Due to its shape, parallel rays of light that pass through it are refracted outwards, away from the principal axis. The emergent rays appear to be coming from a single point behind the lens (the virtual focus). Because it spreads the rays of light apart, it is called a diverging lens.

(j) Deficiency of vitamin A in the body is one of the main causes of night blindness.

Reason: Vitamin A is essential for the synthesis of rhodopsin, a light-sensitive pigment found in the rod cells of the retina. Rod cells are responsible for vision in low-light conditions. A deficiency of Vitamin A leads to insufficient rhodopsin production, impairing the function of the rod cells and causing difficulty seeing in the dark, a condition known as night blindness.

(k) Color blindness occurs when the cone cells of the retina stop functioning.

Reason: The cone cells in the retina are the photoreceptors responsible for detecting color. There are three types of cone cells, each sensitive to different wavelengths of light (red, green, and blue). Color blindness is a genetic condition where one or more types of these cone cells are either missing or do not function correctly. This impairs the brain’s ability to distinguish between certain colors.

4. Write short answers to the following questions.

a. What is the refraction of light?

Refraction of light is the phenomenon of the bending of a light ray as it passes from one transparent optical medium to another. This bending occurs because the speed of light changes as it enters a new medium.

b. Write the laws of refraction of light.

The two laws of refraction are:

The incident ray, the refracted ray, and the normal to the surface at the point of incidence all lie in the same plane.

The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant for a given pair of media. This is known as Snell’s Law:

\(\sin(i) / \sin(r) = \) constant (n)

where n is the refractive index of the second medium with respect to the first.

c. What change is noticed in the shape of a pencil that is half immersed in water as shown in the Figure? Explain with a ray diagram. Write the name of the process associated with this observation.

Change Noticed: The pencil appears bent at the surface where air and water meet. The submerged part of the pencil also appears to be shorter and thicker than the part in the air.

Explanation: This is due to the refraction of light. Light rays from the submerged tip of the pencil travel from water (denser medium) to air (rarer medium) before reaching the eye. As they cross the surface, they bend away from the normal. The eye perceives these bent rays as straight lines originating from a point shallower than the actual tip, making the pencil look bent and raised.

Diagram Description: A diagram would show a glass of water with a pencil in it. Rays of light are drawn from a point on the submerged part of the pencil. As these rays exit the water, they are shown bending away from the normal. Dotted lines trace these refracted rays back to a point above the actual pencil tip, showing the location of the virtual image.

Process: The process is the refraction of light.

d. When a light ray passes from water to air, the angle of incidence and angle of refraction formed at the water-air separation layer are 40.5° and 60° respectively. Draw a ray diagram showing the refraction and write the reason why an object outside appears to be farther away from its actual position when it is viewed by an observer inside the water.

Ray Diagram Description: The diagram would show a horizontal line representing the water-air boundary. A normal (a perpendicular dotted line) is drawn at the point of incidence. A light ray is shown traveling from below (water) and hitting the boundary at an angle of 40.5° to the normal (angle of incidence). The ray then enters the air above, bending away from the normal at an angle of 60° (angle of refraction).

Reason: When an observer inside water views an object in the air, the situation is reversed. Light rays from the object in the air (rarer medium) enter the water (denser medium) to reach the observer’s eye. As the rays enter the water, they bend towards the normal. The observer’s brain interprets these rays as having traveled in a straight line from a point higher, and thus farther away, than the object’s actual position.

e. What is a critical angle?

The critical angle is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium is exactly 90 degrees.

f. What is a total internal reflection of light?

Total internal reflection (TIR) is the phenomenon where a ray of light traveling from a denser medium to a rarer medium is completely reflected back into the denser medium, with no light being refracted into the rarer medium.

g. Write two conditions necessary for total internal reflection of light.

Light must be traveling from an optically denser medium to an optically rarer medium.

The angle of incidence in the denser medium must be greater than the critical angle for the pair of media.

h. At present, data can be transmitted at a very fast rate through fiber internet. Mention the role of total internal reflection of light in fiber internet.

In fiber internet, data is transmitted as pulses of laser light through optical fibers. These fibers are made of a core (denser material) and cladding (rarer material). The light pulses are sent into the core at an angle greater than the critical angle. As the light travels, it repeatedly strikes the core-cladding boundary and undergoes total internal reflection, reflecting back into the core without any loss of intensity. This allows the light signal to travel over very long distances with minimal signal degradation, enabling high-speed data transmission.

i. In endoscopy, colonoscopy and keyhole surgery, how is total internal reflection of light applicable to the devices used to send light to the internal organs of the human body without incisions?

These medical procedures use endoscopes, which consist of a bundle of flexible optical fibers. One bundle of fibers is used to transmit bright light into the body cavity to illuminate it. This light travels down the fibers via total internal reflection. A second bundle of fibers collects the reflected light from the internal organs and transmits the image back to a camera or eyepiece, again using total internal reflection. This allows doctors to view internal organs clearly without making large incisions.

j. What is a dispersion of light?

Dispersion of light is the splitting of white light into its constituent colors (spectrum) when it passes through a transparent medium like a prism. The colors are Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR).

k. Mention the reason for the dispersion of light.

The reason for dispersion is that the refractive index of the medium (e.g., glass) is slightly different for different colors (wavelengths) of light. The speed of light in the medium depends on its wavelength. Violet light (shortest wavelength) travels the slowest and bends the most, while red light (longest wavelength) travels the fastest and bends the least. This difference in bending separates the colors.

l. Draw a ray diagram showing the following processes:

(i) Refraction of light through a glass slab:

Description: A ray of light (incident ray) strikes the top surface of a rectangle (representing the glass slab). It bends towards the normal inside the slab (refracted ray). This ray then strikes the bottom surface and bends away from the normal as it exits (emergent ray). The emergent ray is parallel to the path the incident ray would have taken. The perpendicular distance between these two parallel lines is labeled as the lateral shift.

(ii) dispersion of light through a prism:

Description: A single ray of white light is shown entering one face of a triangle (representing the prism). As it enters, it splits into a band of colors. This band travels through the prism and exits the second face, fanning out even more. The topmost ray is red (least deviated) and the bottommost ray is violet (most deviated), with the other colors in between (VIBGYOR from bottom to top).

m. A person is curious to know why a rainbow always appears semicircular and of the same size. Write down the solution to his curiosity. Include in your answer the position of the sun in the rainbow, the position of the water droplets in the air and the process of dispersion of light.

A rainbow is an optical phenomenon caused by the dispersion and total internal reflection of sunlight by water droplets (like rain or mist) in the atmosphere.

Position of Sun and Observer: To see a rainbow, the sun must be behind you, and the water droplets must be in front of you.

Process: When sunlight enters a water droplet, it first refracts and disperses into its constituent colors. The colors then travel to the back of the droplet and undergo total internal reflection. Finally, they refract again as they exit the droplet, separating the colors further.

Semicircular Shape: Each color exits the droplets at a specific, fixed angle relative to the incoming sunlight (e.g., red at ~42° and violet at ~40°). A rainbow is seen because the observer’s eye intercepts the light from millions of droplets that are all at the correct angle. The collection of all droplets that reflect red light to your eye at 42° forms an arc. The same happens for all other colors, creating concentric arcs. It’s a full circle, but we usually only see the semicircle above the horizon because the ground gets in the way.

n. Define the following terms related to the lens.

(i) Centre of Curvature (C): The center of the sphere of which the lens surface is a part. A lens has two centers of curvature.

(ii) Optical Centre (O): The central point of a lens through which a ray of light passes without any deviation.

(iii) Principal Axis: An imaginary straight line passing through the optical center and the centers of curvature of the lens.

(iv) Focus (F): The point on the principal axis where rays of light parallel to the principal axis either converge (in a convex lens) or appear to diverge from (in a concave lens) after passing through the lens.

o. What is meant by the power of a lens?

The power of a lens (P) is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of its focal length (f) in meters. The unit of power is the dioptre (D).

Formula: P (in D) = 1 / f (in m)

p. The powers of two convex lenses are +2D and +4D respectively.

(i) Which of them is thicker? Give a reason.

The lens with +4D power is thicker.

Reason: Power is inversely proportional to focal length (P = 1/f). A higher power means a shorter focal length. A convex lens with a shorter focal length is more curved and therefore thicker at its center.

(ii) Calculate the focal length of each lens.

For the +2D lens: f = 1 / P = 1 / 2 = 0.5 m or 50 cm.

For the +4D lens: f = 1 / P = 1 / 4 = 0.25 m or 25 cm.

q. In which case is the image formed by a convex lens real and of the same size as the object? Show the ray diagram.

Case: The image formed by a convex lens is real, inverted, and of the same size as the object when the object is placed exactly at twice the focal length (at 2F) from the optical center. The image is also formed at 2F on the other side of the lens.

Ray Diagram Description: An object (an upright arrow) is placed at the point labeled ‘2F’ on the principal axis.

A ray from the top of the object travels parallel to the principal axis and, after passing through the lens, refracts through the principal focus ‘F’ on the other side.

A ray from the top of the object passes through the optical center ‘O’ and goes undeviated.

The two refracted rays intersect at a point below the principal axis. This point is where the top of the image is formed. This intersection point will be exactly at ‘2F’ on the other side, and the resulting image (an inverted arrow) will be the same size as the object.

r. Will the spear thrown by the man shown in the figure, from outside the water hit the fish in the water? Explain it based on the real depth of the fish in the water.

No, the spear will likely miss the fish if aimed directly at its apparent position.

Explanation: Due to refraction, the fish is not where it appears to be. The man sees the fish at an “apparent depth,” which is shallower than its “real depth.” Light rays from the fish travel from water to air and bend away from the normal, making the fish appear higher up. If the man throws the spear directly at the image he sees, the spear will travel in a straight line and pass over the actual position of the fish. To hit the fish, he must aim at a point in the water below where the fish appears to be.

s. What process is shown in the ray diagram? Name any two devices that operate on this process.

(Assuming the diagram shows rays converging to a point or diverging from a point after passing through a lens.)

Process: The process shown is the refraction of light through a lens. If the rays are coming together, it’s a convex lens converging light. If they are spreading out, it’s a concave lens diverging light.

Two Devices:

Camera: Uses a convex lens to form a real, inverted image on a sensor.

Magnifying Glass: A simple convex lens used to produce a magnified, virtual image of a small object.

t. Complete the ray diagram by copying the given figures to the answer sheet.

(This requires drawing. I will describe the completion for standard cases.)

For a Convex Lens:

If a ray is parallel to the principal axis, it will refract through the principal focus (F) on the other side.

If a ray passes through the optical center (O), it will continue in a straight line without deviation.

If a ray passes through the principal focus (F) before hitting the lens, it will emerge parallel to the principal axis.

For a Concave Lens:

If a ray is parallel to the principal axis, it will refract as if it is diverging from the principal focus (F) on the same side.

If a ray passes through the optical center (O), it will continue in a straight line.

If a ray is directed towards the principal focus (F) on the other side, it will emerge parallel to the principal axis.

u. Mention the facts, along with the ray diagram, applicable to the uses of the lens shown in the figure.

(Assuming the figure shows a convex lens being used as a magnifying glass.)

Fact/Use: The figure shows a convex lens being used as a simple microscope or magnifying glass.

Principle: When an object is placed between the optical center (O) and the principal focus (F) of a convex lens, the lens forms a virtual, erect, and magnified image on the same side as the object.

Ray Diagram Description: An object is placed within the focal length (between O and F). A ray from the object’s top parallel to the axis refracts through F on the other side. Another ray from the object’s top goes undeviated through O. These two emergent rays diverge. When extended backward, they appear to meet at a point, forming a larger, upright, virtual image. This allows us to see small objects like text or watch parts enlarged.

v. The given figure shows the dispersion of a light ray through a triangular prism. Answer the following questions based on the given ray diagram.

(a) Which colours of light waves are indicated by X and Y?

(Assuming Y is the top, least deviated ray and X is the bottom, most deviated ray.)

X: Violet

Y: Red

Reason: In dispersion, red light deviates the least, and violet light deviates the most.

(b) Write down the reason why Y is bent less than X when the light rays come out of the prism.

Reason: The amount of bending (refraction) depends on the wavelength of light. Red light (Y) has a longer wavelength than violet light (X). In glass, longer wavelength light travels faster and has a lower refractive index, so it bends less. Shorter wavelength violet light travels slower, has a higher refractive index, and therefore bends more.

w. How can the light dispersed by a prism be converted back into white light?

This can be done by placing a second, identical prism in an inverted position next to the first prism. The first prism disperses the white light into a spectrum. When this spectrum enters the inverted second prism, it recombines the colors through refraction, and a beam of white light emerges from the other side. This experiment was famously performed by Isaac Newton.

x. The focal lengths of the two lenses are 20cm and -20cm respectively. Mention the types of these two lenses. Out of these two lenses, which one forms a virtual and magnified image when an object is kept 16 cm away from the lens? Explain it by drawing a scaled ray diagram.

Lens with f = +20 cm: This is a convex lens (positive focal length).

Lens with f = -20 cm: This is a concave lens (negative focal length).

The lens that forms a virtual and magnified image is the convex lens.

Explanation: A convex lens forms a virtual and magnified image when the object is placed within its focal length. Here, the object distance is 16 cm, which is less than the focal length of the convex lens (20 cm). A concave lens always forms a virtual but diminished image.

Scaled Ray Diagram Description:

Draw a principal axis. Mark the optical center O. Mark the focus F at 20 cm and 2F at 40 cm on both sides.

Place the object (an arrow) at 16 cm from O.

Draw a ray from the top of the object parallel to the axis. After the lens, it refracts through F (at 20 cm) on the other side.

Draw a second ray from the top of the object through the optical center O, which passes undeviated.

The two refracted rays are diverging. Extend them backwards with dotted lines. They will intersect at a point on the same side as the object, farther away than the object. This intersection point is the top of the virtual, erect, and magnified image.

y. Write the functions of the following parts of the eye.

(i) Ciliary muscle: Controls the shape and focal length of the eye lens to focus on objects at different distances.

(ii) Cornea: The transparent outer layer at the front of the eye that does most of the refraction (bending) of light.

(iii) Lens: A transparent, flexible structure behind the iris that fine-tunes the focusing of light onto the retina.

(iv) Iris: The colored part of the eye that controls the size of the pupil, regulating the amount of light entering the eye.

(v) Pupil: The opening in the center of the iris that allows light to enter the eye.

(vi) Retina: The light-sensitive layer at the back of the eye containing photoreceptor cells (rods and cones) that detect light and convert it into neural signals.

z. Write any two problems that may be seen in corneal injury.

Blurred Vision/Astigmatism: An injury can change the smooth, curved shape of the cornea, causing light to focus improperly and leading to blurred or distorted vision (astigmatism).

Scarring and Opacity: A deep injury can lead to scarring, creating an opaque spot on the cornea that blocks light from entering the eye, potentially causing partial or complete blindness in that eye.

27. Explain the role of the ciliary muscle in the change in the thickness of the eye lens when a student sitting in a classroom shifts his eyes from the letters written on the whiteboard to a distant object seen out the window.

This process is called accommodation.

Looking at the Whiteboard (Near Object): To focus on the nearby letters, the ciliary muscles contract. This contraction reduces tension on the suspensory ligaments attached to the lens. The flexible eye lens, being released from tension, becomes more convex (thicker). This decreases its focal length and increases its converging power, allowing it to focus the light from the near object onto the retina.

Looking at the Distant Object: When the student shifts his gaze to a distant object, the ciliary muscles relax. This relaxation increases the tension in the suspensory ligaments, which pull on the lens. The lens is stretched and becomes flatter (thinner). This increases its focal length and decreases its converging power, which is appropriate for focusing the nearly parallel rays from a distant object onto the retina.

28. Identify the type of defect of vision indicated by the given ray diagram. Write two causes of the defect along with its correction.

(Assuming the ray diagram shows parallel rays from a distant object focusing in front of the retina.)

Defect of Vision: Short-sightedness or Myopia.

Two Causes:

Elongation of the eyeball: The distance between the eye lens and the retina is too long.

Excessive curvature of the eye lens: The lens is too converging (has a shorter focal length than normal), causing it to bend light too much.

Correction: This defect is corrected by using spectacles with a concave lens of suitable power. The concave lens diverges the incoming parallel rays of light before they enter the eye. This divergence compensates for the eye’s excessive convergence, effectively moving the focal point backward so that the image is formed correctly on the retina.

29. A student in the class has difficulties in seeing the letters written on the whiteboard when he sits on the last bench but he sees them clearly when he sits on the a first bench. Based on this, answer the following questions:

(i) What type of defect of vision does the student have?

The student has short-sightedness (myopia). He can see nearby objects clearly but not distant ones.

(ii) Draw a ray diagram showing this type of defect of vision of the student.

Description: The diagram would show the eye. Parallel rays of light from a distant object (like the whiteboard from the back bench) are shown entering the eye lens. The lens converges these rays to a point of focus in front of the retina, not on it.

(iii) Write any two reasons for this defect.

The eyeball may be longer than normal.

The converging power of the eye lens may be too high (focal length is too short).

(iv) Explain, with a ray diagram, the role of the lens used to correct this defect.

Explanation: To correct myopia, a concave lens is used. This diverging lens is placed in front of the eye. It spreads out the parallel rays from the distant object before they enter the eye. The eye lens then converges these already diverging rays, and the final image is formed perfectly on the retina.

Ray Diagram Description: First, draw the defective eye showing the image forming in front of the retina. Then, draw a second diagram with a concave lens in front of the eye. The parallel rays from the distant object first diverge slightly at the concave lens. These diverging rays then enter the eye lens, which converges them to a focus exactly on the retina.

30. Explain, with a ray diagram, the role of the lens used to correct long-sightedness.

Defect: In long-sightedness (hypermetropia), a person can see distant objects but not near ones because the image of a near object is formed behind the retina. This happens because the eyeball is too short or the eye lens has too little converging power.

Correction: Long-sightedness is corrected using a convex lens of appropriate power.

Role of the Lens: The convex lens adds to the converging power of the eye’s lens. It pre-converges the light rays from a nearby object before they enter the eye. This extra convergence helps the eye lens to focus the light correctly onto the retina.

Ray Diagram Description: The diagram shows light rays from a nearby object (e.g., at 25 cm). Without correction, these rays would focus behind the retina. With a convex lens placed in front of the eye, the rays are first bent inwards. The eye lens then bends them further, bringing them to a sharp focus precisely on the retina.

31. A student concludes that, ‘the effect of a defect of vision is more on a person wearing spectacles with thick lenses than one wearing that with thin lenses’. Is this understanding correct? Justify with appropriate reasons.

Yes, this understanding is correct.

Justification: The thickness of a lens is directly related to its power. A thicker convex lens or a lens that is much thicker at the edges (concave lens) has a shorter focal length and, therefore, a higher power (since P = 1/f). A higher power is required to correct a more severe vision defect. For example, a person with severe myopia needs a high-power (and thus distinctly shaped/thick-edged) concave lens, while someone with mild myopia needs a low-power (thinner) lens. Therefore, the thickness of the lens is an indicator of the severity of the underlying vision problem.

32. Compare the use of spectacles and the use of contact lenses to correct visual defects.

Feature	Spectacles	Contact Lenses
Placement	Worn in a frame that rests on the nose and ears.	Placed directly on the surface of the cornea.
Field of Vision	The field of view can be limited by the frame.	Provide a full, natural field of vision without obstruction.
Convenience	Easy to put on and take off. Can be inconvenient for sports.	Require careful handling, cleaning, and hygiene. More convenient for sports.
Appearance	Alters the wearer’s appearance. Can be a fashion statement.	Do not alter appearance as they are virtually invisible.
Weather Issues	Can fog up in cold or humid weather and get wet in the rain.	Unaffected by weather conditions.

33. Explain the laser surgery method used to solve eyesight problems.

Laser eye surgery, such as LASIK (Laser-Assisted in Situ Keratomileusis), is a procedure that corrects vision problems like myopia, hypermetropia, and astigmatism by permanently reshaping the cornea.

Procedure:

The surgeon creates a thin, hinged flap in the outer layer of the cornea.

This flap is lifted to expose the underlying corneal tissue (stroma).

An excimer laser, which emits cool ultraviolet light, is used to remove a microscopic amount of tissue from the stroma, precisely reshaping it. For myopia, the cornea is flattened; for hypermetropia, it is made steeper.

The corneal flap is then placed back in its original position, where it heals naturally without stitches.

By changing the cornea’s shape, the surgery adjusts how light is focused on the retina, correcting the refractive error.

34. What is a cataract? Write the role of the intraocular lens developed by Nepal’s ophthalmologist Dr. Sanduk Ruit in the treatment of cataracts.

Cataract: A cataract is a medical condition in which the natural lens of the eye becomes progressively opaque or cloudy, resulting in blurred vision and eventual blindness if untreated.

Role of Intraocular Lens (IOL): Dr. Sanduk Ruit pioneered a revolutionary, low-cost method for cataract surgery. His technique, known as sutureless small-incision cataract surgery, involves removing the cloudy natural lens through a small incision. An intraocular lens (IOL), which is a small, artificial lens, is then inserted into the eye to replace the natural lens. Dr. Ruit’s team also developed high-quality, very low-cost IOLs, making this sight-restoring surgery affordable for millions of impoverished people worldwide. The IOL takes over the function of the natural lens, focusing light onto the retina and restoring clear vision.

5. Solve the following mathematical problems.

(a) If the speeds of light in air and glass are 3×10⁸ m/s and 2×10⁸ m/s respectively, then calculate the refractive index of glass with respect to air.

Given: v_air = 3×10⁸ m/s, v_glass = 2×10⁸ m/s

Formula: n_glass = v_air / v_glass

Calculation: n_glass = (3×10⁸) / (2×10⁸) = 1.5

Answer: The refractive index of glass is 1.5.

(b) The refractive index of a diamond is 2.42. If the speed of light in air is 3×10⁸ m/s, calculate the speed of light in a diamond.

Given: n_diamond = 2.42, v_air = 3×10⁸ m/s

Formula: n_diamond = v_air / v_diamond ⇒ v_diamond = v_air / n_diamond

Calculation: v_diamond = (3×10⁸) / 2.42 ≈ 1.239×10⁸ m/s

Answer: The speed of light in a diamond is approximately 1.24×10⁸ m/s.

(c) When a ray of light falls on the surface of a plastic block, the angle made by the ray with the normal and the angle of refraction are found to be 45° and 33° respectively. Calculate the refractive index of that plastic.

Given: i = 45°, r = 33°

Formula: n = sin i / sin r

Calculation: n = sin 45° / sin 33° = 0.7071 / 0.5446 ≈ 1.298

Answer: The refractive index of the plastic is approximately 1.3.

(d) Calculate the power of a lens having a focal length of 25 cm.

Given: f = 25 cm = 0.25 m

Formula: P = 1 / f

Calculation: P = 1 / 0.25 = 4 D

Answer: The power of the lens is +4 D (converging lens).

(e) The power of the lens used in the spectacles worn by a student is -6 D. Calculate the focal length of the lens. Also, mention the type of lens.

Given: P = -6 D

Formula: f = 1 / P

Calculation: f = 1 / -6 = -0.1667 m = -16.67 cm

Answer: The focal length of the lens is -16.67 cm. Since the focal length is negative, it is a concave lens.