Class 10 Wave Exercise 10.1 Solutions | Science and Technology Curriculum Development Centre

The differences between reflection of light and total internal reflection of light are as follows:

The major differences between concave lens and convex lens are:

The differences between near point and far point of the eye are:

Differences between color blindness and night blindness are as follows:

Between glass and water, glass is a denser medium and water is a rarer medium.

Light bends when it passes from one medium to another medium due to change in its velocity. When passed through glass to water, the light after refraction travels faster in water and moves away from the normal.

Light travels faster in rarer density having medium. Hence, water is rarer medium and glass is denser medium between water and glass.

When a coin is placed at the bottom of a glass containing water, it appears to rise due to the phenomenon of refraction of light. 

When an object is placed in the denser medium and it is viewed from rarer medium then it seems to be at less depth than the actual depth.

In this case, the water is the denser medium and air is the rarer medium. This refraction makes the coin appear to be at a higher position than its actual location at the bottom of the glass.

When you look at letters on paper through a glass slab, they appear slightly raised because of refraction.

Refraction occurs when light travels from one medium to another, such as from air into glass. Light moves at different speeds in different materials.

When light moves from the paper through the glass slab to your eyes, it bends, making the letters seem closer to the surface than they actually are. This creates an illusion that the letters are raised, even though they’re at the same place on the paper.

The light from the stars passes through the atmosphere before it reaches the observer on earth. Atmosphere has layers of air with different densities. Due to the current of air, the densities of the layer of air, keep on changing continuously. 

This causes the position of the image of star to change continuously with time in space. As the change in density is in a small range, the image of star appears to move within a small area in the space due to refraction of light of the stars.

This gives rise to their twinkling effect.

The phenomenon where the sun appears on the horizon about two minutes before the actual sunrise is primarily due to atmospheric refraction. 

As sunlight passes through the Earth's atmosphere, it bends or refracts because of the varying densities of air layers. This bending causes the light rays from the sun to reach an observer's eyes even when the sun is geometrically below the horizon. 

This effect can make it seem as though the sun has risen before it truly has, resulting in a visual perception of sunrise occurring a couple of minutes earlier than the actual event.

A diamond has more refractive index (2.4>1.5) and less critical angle(24°<42° ) as compared to  glass.

A diamond is cut in a special way such that many total internal reflections take place inside it. After multiple such reflections, the colors in the light are separated and seen individually. This phenomenon causes the diamond to shine in dim light as well.

However, such is not possible for glass due to its inability to bend light as compared to diamond. Hence, a diamond appears to shine but a piece of glass cut to the same shape does not shine.

Sunlight is refracted when it passes through a prism because of the change in speed of light as it moves from one medium to another.

Sunlight is white light consisting of seven different colors which have different velocities in a denser medium due to their different magnitudes of wavelength. When light enters the prism from air (a less dense medium) into glass (a denser medium), it slows down and bends towards the normal line. This bending occurs at both the entry and exit points of the prism.

Since a prism has angled surfaces, the light rays do not exit parallel to their original direction; instead, they are deviated, resulting in a separation of colors due to different wavelengths of light being refracted by varying amounts. This phenomenon is known as dispersion of light, where white light splits into its constituent colors, creating a spectrum.

A convex  lens is thicker at its middle and thinner at the edges.

A convex lens converges light rays due to its specific shape and the principles of refraction. In a convex lens, when a parallel beam of light is incident, the lens converges it to a point after the refraction.

Thus, a convex lens converges light rays and is known as converging lens.

A concave lens is thinner at its middle and thicker at the edges.

A concave lens diverges light rays due to its specific shape and the principles of refraction. In a concave lens, when a parallel beam of light is incident, the lens make the rays appear to be diverged from a point after the refraction.

Thus, a concave lens diverges light rays and is known as diverging lens.

Night blindness means difficulty seeing in low light or darkness.

Disorder of rods cells causes night blindness. Vitamin A plays a crucial role in the formation of rhodopsin, a photopigment found in the rod cells of the retina that is essential for vision in low-light conditions. Moreover, vitamin A plays a role in transforming  nerve impulses into images in the retina.

Hence, deficiency of vitamin A in the body is one of the main causes of night blindness. 

There are different types of cone cells called red cone cells, blue cone cells and green cone cells on the retina. 

When one or more types of cones are missing or malfunctioning, the brain receives incomplete or altered signals about color, leading to difficulties in distinguishing between colors. This deficiency in cone function disrupts the normal processing of color information, resulting in the characteristic symptoms of color blindness. 

Due to disorder on these cone cells, a person suffers from color blindness. 

The phenomenon of bending of light when it passes from one medium to another is called refraction of light.

Light bends when it passes from one medium to another medium because of change in velocity.

Light travels faster in rarer density having medium.

The laws of refraction of light are as follows:

•  The incident ray, refracted ray and normal lie in the same plane.
• Light bends towards the normal when passing from rarer to denser medium, and bends away from the normal when passing from denser to rarer medium.
• The ratio of sine angle of incidence to the sine angle of refraction is always constant. This law is known Snell's law.

\(\rm µ\)= $\frac{sin i}{sin r}$

• When light ray incidents normally, it passes without bending.

The angle of incidence for which the angle of refraction is 90$^o$ when a ray of light passes from a denser medium to a rarer medium is defined as the critical angle for the given pair of media.

When a ray of light travels from a denser medium to a rarer medium, it has the possibility of undergoing total internal reflection instead of refraction. The maximum angle that a ray of light can make when going from a denser medium to a rarer medium without undergoing total internal reflection is called a critical angle.

When angle of incidence in a denser medium is greater than critical angle, the light does not refract, instead it reflects back to the same medium.

This phenomenon is called total internal reflection of light.

The two conditions necessary for the total internal reflection of light are as follows:

1. The ray of light must be passing from a denser medium to a rarer medium.
2. The angle of incidence in the denser medium ($\rm i$) must be greater than the critical angle $\rm i_{c}$.

In fiber internet, data is transmitted as light signals through thin glass or plastic fibers. These signals travel using a process called total internal reflection. 

When light moves through the fiber and hits the boundary between the fiber's core (where light travels) and the outer layer (cladding), it hits at an angle that makes it reflect back into the core instead of escaping. This angle has to be greater than a certain critical angle for total internal reflection to occur.

Because of this, the light keeps bouncing along the fiber, even if the fiber bends slightly, allowing data to travel over long distances quickly and efficiently. 

This is why fiber optic cables are so effective at delivering high-speed internet over vast distances.

In procedures like endoscopy, colonoscopy, and keyhole surgery, doctors use thin, flexible tubes called fiber optic scopes to see inside the body without large incisions. Inside these scopes, fiber optic cables transmit light to illuminate internal organs.

Total internal reflection makes this possible. When light enters the fiber, it reflects off the inner walls without escaping, as long as it hits at an angle greater than the critical angle. This allows the light to travel down the length of the fiber, even if it bends, reaching deep areas inside the body. This reflected light also brings back images, letting doctors see and examine tissues in real time, which helps in diagnosing and treating conditions with minimal invasive procedures.

When a beam of white light is passed through a prism , it splits into its seven constituent colors: red, orange, yellow, green, blue, indigo and violet.

This phenomenon of splitting white light into its constituent colors is called dispersion of light.

The dispersion of light takes place due to reasons given as follows:

Variation in Wavelengths: Different colors in white light have different wavelengths. Shorter wavelengths (like blue and violet) slow down more than longer wavelengths (like red) when passing through a medium.

Change in Speed: When light enters a denser medium, each color bends (refracts) by a different amount based on its speed. Shorter wavelengths bend more, causing the separation of colors.

Refractive Index: Each color has a slightly different refractive index in the same medium, which leads to each color traveling at a slightly different angle and speed, spreading out to form a spectrum.

Hence, red light has maximum speed and deviates the least while violet light had minimum speed and deviates the most. The deviations of other colors occupy intermediate positions between the violet and red colors. 

Refraction of light through a glass slab occurs when light passes from air into the glass, slowing down and bending toward the normal line at the surface. Inside the glass, the light travels more slowly in a straight line until it reaches the opposite surface. As it exits back into the air, it speeds up again and bends away from the normal. This bending of light causes objects viewed through the glass slab to appear slightly raised or shifted, as the light takes a different path than it would have in air.

Above diagram shows the dispersion of light through a prism.

The band of seven colors formed on a screen as a result of dispersion is called the spectrum.

Red is the least deviated while violet is the most deviated.

A rainbow appears semicircular and of consistent size due to the interaction of sunlight with water droplets in the air, combined with the observer’s viewpoint.

Position of the Sun: The sun must be positioned behind the observer for a rainbow to be visible. The light from the sun enters water droplets in the air, which act as tiny prisms.

Position of Water Droplets: Water droplets in the atmosphere are roughly spherical. As sunlight enters each droplet, it undergoes refraction (bending), dispersion (separating into colors), internal reflection, and then refraction again as it exits. This dispersion splits the white light into a spectrum of colors.

Process of Dispersion: When light enters the droplet, shorter wavelengths (like blue and violet) bend more than longer wavelengths (like red). This creates a color separation. After internal reflection inside the droplet, the light exits and bends again, forming a spectrum.

Semicircular Shape: The rainbow appears semicircular because the droplets refract light at a specific angle (about 42 degrees for red light and slightly less for blue light) relative to the incoming sunlight. 

From the observer’s perspective, only droplets positioned at this angle from the line of sight reflect light into their eyes, forming a circular arc. Since the ground obstructs the lower part, we usually see only a semicircle.

Consistent Size: The size of the rainbow remains consistent because the 42-degree angle is fixed; thus, a rainbow appears roughly the same size no matter where or when it is observed.

The center of the spheres from which the lens is made is called center of curvature of a lens.

It is denoted by C or 2F.

The middle point of refracting surface of the lens is called its optical center.

It is denoted by O.

The imaginary line that joins the centers of curvature through the optical center is called principle axis of a lens.

The point on the principle axis where rays of light parallel to principle axis converge or appear to be diverged from is called focus or principle focus of a lens.

It is denoted by F.

Power of a lens is defined as the reciprocal of the focal length expressed in meters.

\(\rm Power\) \(\rm of\) \(\rm lens \) = $\frac{1}{ f(in m)}$

\(\rm P\)= $\frac{1}{f}$

where, f= focal length

The S.I. unit of power of lens is diopter (D)

When an object is placed at 2F, the image is formed by the convex lens at 2F of the lens. The image is real, inverted and of the same size of the object.

Ray diagram:

When the light dispersed by a prism is passed through another inverted prism as shown in figure below, all the colors mix with each other and white light emerges out from the prism. This is called recombination of the colors.

In this way the light dispersed by a prism be converted back into white light.

Here,

The the lens with the focal length 20 cm is a convex lens as its focus is real.

Ans, the lens with focal length -20 cm is a concave lens as its focus is virtual.

The lens with focal length 20cm i.e. a convex lens forms a virtual and magnified image when the object is kept 16 cm from the lens. When a object is placed between focus(F) and optical center(O) of a convex lens it forms a virtual and magnified image.

Here, the distance of object is 16cm i.e. between F and O. So, a convex mirror can form virtual and magnified image with given condition.

Ray diagram:

The function of the ciliary muscle in the human eye is to alter the focal length of the lens of the eye to make the eyes able to see near and distant objects by the same lens.

The cornea is the transparent front layer of the eye that refracts light, helping to focus images on the retina. It also serves as a protective barrier against dust, germs, and other harmful elements.

Behind the iris, there is a important crystalline, transparent convex lens. It converges the light reflected from objects on the retina to form their real, inverted and diminished images. The single eye lens in each eye is used to see both close and distant objects.

The front part of the choroid forms colored iris. The iris has a hole at the center which is  called the pupil. Iris controls the amount of light required to enter into the eyes.

The pupil in present in the human eye right after iris in front part of choroid.

Iris enlarges in dark and shrinks in bright light. The pupils allow the light to pass in the eyes.

The inner layer of the eyeball is called retina. It is sensitive to light.

The retina prevents internal reflection. Retina is where the images are formed. Retina is connected with the brain through the optic nerves. The images formed is carried to brain by the optic nerves.

Corneal injury occurs when the surface of the cornea is torn, scratched or scraped from an outside object like contact lens, flying glass, plants, twigs or others.

Any two problems that may be seen in corneal injury are:

• This is a scratch or injury to the surface of the cornea that can cause pain, redness, tearing, and sensitivity to light, potentially leading to infection if not treated properly.
• A superficial injury seldom leads to permanent vision loss.

The ciliary muscle is a ring of smooth muscle in the eye that controls the shape of the lens to facilitate focusing on objects at varying distances. 

When a student shifts their gaze from the whiteboard to a distant object, the ciliary muscle relaxes, causing the lens to become thinner for distant vision. This reduction in thickness allows light rays from faraway objects to be properly focused on the retina, ensuring clear vision.

Conversely, when focusing on nearby objects, the ciliary muscle contracts, thickening the lens for better clarity.

1.Ans:

According to the questions, the student finds it hard to see letters from a distance but is able to see them from short distance.

Hence the student has short-sightedness or myopia.

3.Ans:

Two reasons for this defect are:

• Shortening of focal length of eye
• The eye is too long or oval-shaped rather than round.

2.Ans:

Diagram:

4.Ans:

The above diagram shows the role of of the lens used to correct this defect.

Concave lens of suitable focal length should be used to correct this defect. The lenses diverge the rays passing from distant objects to retina. Hence, clear image of distant objects is formed after the use of concave lens.

In long-sightedness or hypermetropia, the eye can form the image of distant objects on the retina but the image of closer objects is formed behind the retina.

For the correction of this defect, convex lens spectacles or contact lenses of suitable focal length are used. The lenses converge the light rays passing from closer objects which are again converged by the lens on the retina.

In this way, convex lens are used to correct long-sightedness.

The student’s conclusion is mostly correct. Thicker lenses generally indicate a stronger prescription, which corresponds to a greater degree of vision defect. People who require high-prescription lenses usually experience more severe refractive errors, like stronger nearsightedness or farsightedness, which these thick lenses are designed to correct.

Thicker lenses also tend to create more peripheral distortion, especially around the edges of the glasses. This can make the visual experience less natural, as objects may appear distorted or “stretched” near the lens edges, which isn’t as pronounced with thinner lenses.

In addition, thick lenses are usually heavier, which can cause discomfort for the wearer. Heavier glasses can put strain on the nose and ears, making them less comfortable to wear for long periods. However, modern lens technology, like high-index lenses, can make lenses thinner even for strong prescriptions, reducing these issues.

Both spectacles (glasses) and contact lenses are popular ways to correct visual defects, such as nearsightedness, farsightedness. Here’s a comparison between the two:

Comfort and Convenience

• Spectacles: Easy to put on and take off, but they can slip off, fog up, or be uncomfortable during physical activities. They’re generally less convenient for sports or strenuous activities.
• Contact Lenses: They provide a natural field of view and don’t fog up, making them ideal for physical activities. However, they can be uncomfortable for some people, especially if worn for long periods or in dry environments.

Maintenance and Care

• Spectacles: Require minimal care, just regular cleaning with a cloth and possibly adjustments by an optician. They are generally easier to maintain.
• Contact Lenses: Need daily cleaning and proper storage to avoid infections. Mismanagement can lead to eye infections or dryness, making care more time-consuming.

Cost

• Spectacles: Typically, they are a one-time expense that can last for years, though they might need replacements if damaged or prescriptions change.
• Contact Lenses: Depending on the type (daily, weekly, or monthly disposables), they can be more expensive over time due to the need for regular replacements and cleaning supplies.

Laser eye surgery, commonly known as LASIK (Laser-Assisted In Situ Keratomileusis), is a procedure used to correct vision problems like nearsightedness, farsightedness, and astigmatism. 

In this method, a specialized laser reshapes the cornea (the clear front part of the eye) to allow light entering the eye to be properly focused on the retina, thus improving vision clarity. The surgery begins with creating a thin flap on the cornea's surface, which is then lifted to allow the laser to reshape the underlying corneal tissue precisely. 

After the cornea is reshaped to correct the specific refractive error, the flap is placed back, where it naturally adheres without stitches. This procedure is quick, typically painless due to numbing eye drops, and has a short recovery time, with many patients noticing improved vision within a day.

Cataracts are an eye condition when the lens of the eye develops cloudy patches of protein that obstructs passage of light in the lens. Over time, these patches usually grow bigger causing blurry vision.

Cataract surgeries are conducted for the treatment of cataract. the procedure usually takes as little as 20 minutes to complete. Nepal's opthalmologist Dr. Sanduk Ruit developed very cheap intra-ocular lens(IOL). Dr. Sanduk Ruit’s affordable intraocular lens revolutionized cataract treatment by providing a low-cost, high-quality solution to replace clouded lenses, restoring vision for cataract patients. This innovation made cataract surgery accessible in low-resource settings, helping millions worldwide regain their sight. For such great contribution, he is honored with many national and intenational awards.

Given:

Speed of light in air ( c ) : \(\rm 3 × 10^{8} m/s \)

Speed of light in glass ( v ) : \(\rm 2 × 10^{8} m/s\)

The refractive index of glass with respect to air ( \(\rm µ \) ) is given by:

\(\rm µ \)= $\frac{c}{v}$

\(\rm or,\)\(\rm µ \)= $\frac{3 × 10^{8}}{2 × 10^{8}}$

\(\rm or,\)\(\rm µ \) = $\frac{3}{2}$

\(\rm or,\)\(\rm µ \) = \(\rm 1.5 \)

Thus, the refractive index of glass with respect to air is 1.5.

To calculate the power of lens we use the formula:

\(\rm P \) = $\frac{1}{f}$

where \(\rm P\) = Power of lens

and,   \(\rm f\) = focal length of lens

For f= 25cm = 0.25m :

\(\rm P \) = $\frac{1}{f}$

\(\rm or,\) \(\rm P\) = $\frac{1}{0.25}$

\(\rm or,\) \(\rm P \) = \(\rm 4\)

Hence, for lens with focal length 25cm power of lens is +4D.