Nootan solutions for Physics Part 1 and 2 [English] Class 12 ISC chapter 15 - Refraction of Light at a Plane Interface : Total Internal Reflection : Optical Fibre [Latest edition]

Refractive index of a transparent material is ______.

When monochromatic light passes from a vacuum to a material medium and vice versa, which of the following characteristics of the light beam does not change?

When a light wave travels from air to glass ______.

A diver from inside the water `(n = 4/3)` looks at an object in the air whose natural colour is green. He sees the object as ______.

Monochromatic light is refracted from air into a medium of refractive index n. The ratio of the wavelengths of the incident and the refracted waves is ______.

A light ray passes from a vacuum into a medium of refractive index n. The angle of refraction is found to be half the angle of incidence. The angle of incidence is ______.

A piece of glass immersed in a colourless liquid is not visible. It is so because ______.

The refractive indices of glass and water with respect to air are `3/2` respectively. The refractive index of glass with respect to water will be ______.

When a glass slab of refractive index 1.5 is placed on a cross marked on paper, the cross appears to be raised by 2 cm. The thickness of the slab is ______.

It is possible to observe total internal reflection when light travels from ______.

The velocity of light in a medium is 1.5 × 10⁸ ms⁻¹. The critical angle C for a ray going from the medium into air is ______.

The critical angle will be largest when light goes from ______.

A swimmer inside water looks up at the sky through the surface of the water. The sky is bright due to daylight. He can see ______.

A fish which is at a depth of 12 cm in water `(n = 4/3)` is viewed by an observer on the bank of a lake. The apparent depth as observed by the observer is ______.

Light passes from air to glass and is deviated 3.5°. When the angle of incidence is 10°, the refractive index of the material of the glass is ______.

A bird in the air looks at a fish vertically below it and inside the water in a tank. If the distance of the fish as estimated by the bird is x₁ and that of the bird as estimated by the fish is x₂, then the refractive index of water is ______.

Why does refraction of light occur when light passes from one medium to another?

Does frequency change when light passes from one medium to another?

Define the refractive index of glass in terms of the speed of light.

Can the absolute refractive index of a medium be less than one?

Can the refractive index of a medium relative to another medium be less than 1?

Define critical angle for a given medium.

Find a critical angle for a glass and water pair, given the refractive index of glass is 1.62 and that of water is 1.33.

A microscope is focused on a dot at the bottom of a beaker. Oil is poured into the beaker to a height of y cm. Now, the microscope is to be raised through a vertical distance of x cm to bring the dot again into focus. Express the refractive index of oil in terms of x and y.

Does critical angle depend upon the colour (wavelength) of light used?

Is the critical angle for a given interface greater for red light or for blue light?

What is the critical angle for a material of refractive index `sqrt2` relative to air?

Will the critical angle for the glass-water interface be smaller or larger than that for the glass-air interface?

What is the refractive index of diamond?

What is the critical angle of diamond?

Which has a larger critical angle, water or diamond?

Name the phenomenon responsible for mirage.

Name the principle on the basis of which optical fibres work.

Discuss refraction through a glass slab and show that the emergent ray is parallel to the incident ray but displaced.

For what angle of incidence, the lateral displacement is maximum? Can it be zero?

A beam of light is converging towards a point. A parallel-sided glass slab is introduced in the path of this beam. How will the point of convergence be shifted? Draw the ray diagram.

Define the critical angle for an interface of two media.

What is total internal reflection? 

State two conditions necessary for total internal reflection to occur.

Can total internal reflection occur when light travels from a rarer to a denser medium?

What is meant by the term ‘critical angle’?

Give one application of total internal reflection.

What are optical fibres?

Give one use of optical fibres?

Show, with a diagram, how an image is produced in a totally reflecting prism.

What are the advantages of a totally reflecting prism over a plane mirror?

For the same value of angle of incidence, the angles of refraction in three media A, B and C are 15°, 25° and 35°, respectively. In which medium would the velocity of light be minimum?

A diver underwater looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?

A straight stick partly dipped in water obliquely appears to be bent at the surface of the water.

The sun begins to be seen a little before it rises and continues to be seen for several minutes after it has actually set. Explain.

Sun (or moon), when near the horizon, appears elliptical and not circular. Explain why?

Why do stars appear twinkling?

An empty test tube dipped obliquely into water appears silvery when viewed in a suitable direction. Why?

The refractive index of diamond is much greater than that of glass. Does a diamond cutter use this fact?

Draw a diagram to show how an image is produced by a pair of total reflecting prisms arranged as in a periscope.

State the law of refraction.

Distinguish between absolute refractive index and refractive index of a medium.

Show that n = `c/v`, where letters have usual meanings.

Explain why does a swimming pool appears shallower than it actually is.

Obtain an expression for the normal displacement of an object immersed in water.

With a neat ray diagram, explain the concept of total internal reflection (TIR). 

State two conditions necessary for total internal reflection to occur.

Obtain the relation between the critical angle and the refractive index of the denser medium.

Show, with a diagram, how an image is produced in a totally reflecting prism.

What is an optical fibre?

Name the principle on the basis of which optical fibres work.

Explain, by ray diagram, how optical fibres transmit signals.

Mention one practical application of optical fibres.

What is refraction of light?

State the law of refraction.

Derive the relation n = `"Real depth"/"Apparent depth"`.

What form does it take when the object is viewed through several media?

Define the reversibility of light.

Define the refractive index.

Prove that ₁n₂ × ₂n₃ × ₃n₁ = 1.

Can the absolute refractive index of a medium be less than one?

A vessel of depth d is filled upto a depth of d₁ by a liquid of refractive index n₁ upto a depth of d₂ by a liquid of refractive index n₂ and upto a depth of d₃ by a liquid of refractive index n₃. Show that the apparent depth of the vessel when viewed normally is given by:

`h_(app) = (d_1/n_1 + d_2/n_2 + d_3/n_3)`

[here d = d₁ + d₂ + d₃ and n₁ > n₂ > n₃]

Read the passage given below and answer the questions that follow:

Critical angle for glass-air interface can be written as

`sin i_c = 1/(""_an_g) = "velocity of light in glass"/"velocity of light in air"`

1. Name the principle on the basis of which optical fibres work.
2. Calculate the critical angle for the glass and water pair. Given the refractive index of glass is 1.62 and that of water is 1.33.
3. A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is `4/3` (n = 3.14).
4. 
   
   Light rays of blue, green and red colours are incident on a right-angled prism, as shown. Green ray makes a grazing emergence. Out of red and blue light, which one comes out of the prism without suffering total internal reflection?

The refractive index of diamond relative to air is 2.42 and that of glass is 1.51. How much faster does light travel in glass than in diamond?

A ray of light in air is incident on a glass plate at 45°. The refractive index of glass is 1.5. What is the angle of refraction?

A ray of light which is incident in air on the surface of a glass block is deviated through 15°. The angle of incidence in air is 60°. What is the angle of refraction in glass? Also calculate the critical angle for the glass-air interface.

How deep will a 4 m deep tank appear when seen in air due to optical refraction? The refractive index of water is `4/3`.

A beaker is filled with water to a height of 12.5 cm. The apparent depth of a needle at the bottom of the beaker is 9.4 cm. Find the refractive index of water.

The apparent depth of an object at the bottom of a tank filled with a liquid of refractive index 1.3 is 7.7 cm. What is the actual depth?

A needle lying on a horizontal surface is viewed vertically from a distance of 100 cm. A glass slab of 12 cm thickness is placed on the needle. Find the distance of the vertical image of the needle from the eye, taking _an_g = 1.5.

A microscope focused on a pin lying at the bottom of a beaker reads 3.965 cm. When a liquid is poured up to a height of 2.537 cm into the beaker, the microscope focused again on the pin reads 3.348 cm. Find the refractive index of the liquid.

A beaker is filled with a liquid to a height of 14 cm. The apparent depth of a needle fixed at the bottom of the beaker is measured to be 10 cm by a microscope. What is the refractive index of the liquid? The height of the liquid in the beaker is now raised to 21 cm. By what distance would the microscope have to be moved to focus on the needle again?

A beaker 20 cm high is half filled with an oil of refractive index 1.40 and the upper half filled with water of refractive index 1.33. What is the apparent depth of the beaker as observed normally?

A beaker is filled with water (n = 1.5) to a height h. Height of the beaker is 15 cm. When the bottom of the beaker is viewed vertically by an observer, the beaker appears to be half filled. Find the value of h.

A container of uniform cross-section has a height of 14 m. Upto what height should water of refractive index `4/3` be filled inside the container so that the container seems to be half filled for normal viewing?

In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?

Critical angle for total internal reflection from a medium to a vacuum is 60°. Find the velocity of light in the given medium.

A ray of light falls normally on the face of a glass prism (n = 1.5). Find the angle of the prism if the ray just fails to emerge from the second face.

A substance has a critical angle of 45° for yellow light. What is the refractive index of the substance?

The refractive index of glass relative to air is 1.5. What is the critical angle for the glass-air interface?

What is the critical angle for a light ray going from dense glass into water? The refractive indices of dense glass and water relative to air are 1.62 and 1.33 respectively.

The absolute refractive indices of water and glycerine are 1.33 and 1.46 respectively. Find the critical angle for a ray travelling from glycerine into water.

An equilateral prism of glass of refractive index 1.45 is immersed in water of refractive index 1.33. A narrow beam of light falls normally on one face of the prism. Find the angle of emergence of the beam.

A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

A point source of light is placed at the centre of the bottom of a jar having a liquid of refractive index `5/3`. An opaque disc of radius 1.0 cm is placed on the liquid surface with its centre vertically above the source. What is the maximum height of the liquid for which the source is not visible from above?

Name the principle on the basis of which optical fibres work.

State one advantage in the use of optical fibres.

Draw a diagram to show how an image is produced by a pair of total reflecting prisms arranged as in a periscope.

A ray of light is normally incident on one face of an equilateral prism. Trace the course of the ray through the prism and emerging from it.

Find the refractive index of the liquid if a ray of light strikes surface AB normally and then comes out from face AC at grazing emergence. `(""_aμ_g = 3/2)`

A fish is located at a distance of 10 cm from the wall of the fish pond. The thickness of the glass wall is 2 cm. Find the apparent position of the fish. `("Given"  ""_aµ_g = 3/2  "and"  ""_aµ_w = 4/3)`

A point source of monochromatic light S is kept at the centre C of the bottom of a cylinder. The radius of the circular base of the cylinder is 15.0 cm.

The cylinder contains water `("Refractive index" = 4/3)` to a height of 7.0 cm, as shown in the figure. Find the area of the surface through which light emerges in air. `("Take", π = 22/7)`

A ray LM of monochromatic light incident normally on one refracting surface AB of a regular glass prism ABC emerges in air from the adjacent surface AC as shown in the figure. Calculate the refractive index of the material of the prism.

Calculate the critical angle for the glass and water pair. (Take refractive index for glass is 1.50 and the refractive index for water is 1.33.)

A ray of light LM incident normally on the surface AC of an isosceles right angled prism ABC (where AB = BC) emerges along PQ, parallel to LM, as shown in the figure below. What can you say about the refractive index µ of the material of the prism?

At what angle, a ray of light should be incident on the first face AB of a regular glass prism ABC, so that the emergent ray grazes the adjacent face AC? (Refractive index of glass = 1.6)

 A narrow beam of monochromatic light, PQ, is incident normally on one face of an equiangular glass prism of refractive index 1.45. When the prism is immersed in a certain liquid, the ray makes a grazing emergence along the other face (See figure). Find the refractive index of this liquid. 

A fish which is at a depth of 12 cm in water `(mu = 4/3)` is viewed by an observer on the bank of a lake. Its apparent depth as observed by the observer is ______.

Find a critical angle for a glass and water pair, given the refractive index of glass is 1.62 and that of water is 1.33.

When a light wave travels from air to glass ______.

Define critical angle for a given medium.

Name the principle on the basis of which optical fibres work.

An observer can see the top end B of a thin rod of height h through a pin-hole. The height of the beaker is 3h, and the radius is h. When the beaker is filled with a liquid up to a height of 2h, the observer can see the lower end A of the rod. The refractive index of the liquid is:

An air bubble in a glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is ______.

A container is filled with water (n = 1.33) up to a height of 33.25 cm. A concave mirror is held 15 cm above the water level, and the image I of an object O placed at the bottom is formed 25 cm below the water level. The focal length of the mirror is roughly:

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is `4/3`. A fish inside the lake, in the line of fall of the ball is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as ______.

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is ______.

A light beam is travelling from Region I to Region IV as shown in the figure below: The refractive indices of Regions I, II, III and IV are `n_0, n_0/2,n_0/6` and `n_0/8` respectively. The angle of incidence θ for which the beam just misses entering Region IV is:

A green light is incident from the water to the air-water interface at the critical angle (C). Select the correct statement.

The velocity of light in transparent media A and B separated by a plane boundary are 2.0 × 10⁸ and 2.5 × 10⁸ ms⁻¹ respectively. The critical angle for a light ray passing from A to B at the boundary is ______.

A beam of light consisting of red, green and blue colours is incident on a right-angled prism, as shown. The refractive indices of the material of the prism for the red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will ______.

A glass prism of refractive index 1.5 is immersed in water `("refractive index" = 4/3)`. A light beam is incident normally on the face AB. It will be totally reflected at the face AC to reach the face BC, if:

A light ray travelling in a glass medium is incident on a glass-air interface at an angle of incidence of θ. The reflected (R) and transmitted (T) intensities, both as functions of θ, are plotted. The correct sketch is:

A ray of white light is incident on the interface of glass and air, as shown. The angle of incidence is such that green light just suffers total internal reflection. The ray of light emerging from glass to air contains:

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then, there will be ______.

A transparent solid cylindrical rod has a refractive index of ​`2/sqrt3`​. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is ______.

The angle of a prism is ‘A’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence of 2A on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index, n, of the prism is ______.

A ray of light AO in a vacuum is incident on a glass slab at an angle of 60° and refracted at an angle of 30° along OB as shown in the figure. The optical path length of the light ray from A to B is ______.

In the figure, the optical fibre is l = 2 m long and has a diameter of d = 20 µm. If a ray of light is incident on one end of the fibre at angle θ₁ = 40°, the number of reflections it makes before emerging from the other end is close to:

(Refractive index of fibre is 1.31 and sin 40° = 0.64)

A transparent cube of side, made of a material of refractive index n₂, is immersed in a liquid of refractive index n₁ (n₁ < n₂). A ray is incident on the face AB at an angle θ (shown in the figure). Total internal reflection takes place at point E on the face BC. Then θ must satisfy:

In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?

Pick the wrong answer in the context with rainbow.

A light wave is incident normally on a glass slab of refractive index 1.5. If 10% of light gets reflected and the amplitude of the electric field of the incident light is `30 V/m`, then the amplitude of the electric field for the wave propagating in the glass medium will be:

A concave mirror has a radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen from directly above the glass is at a distance d from the surface of water. The value of d is dose to: (Refractive index of water = 1.33)

If the critical angle for total internal reflection from a medium to a vacuum is 45°, then the velocity of light in the medium is ______.

A wide slab consisting of two media of refractive indices n₁ and n₂ is placed in air as shown in the figure. A ray of light is incident from medium n₁ to n₂ at an angle θ, where sin θ is slightly larger than `1/n_1`. Take the refractive index of air as 1. Which of the following statement(s) is(are) correct?

A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal surface separating medium with air. The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium will be:

[Given relative permeability of the medium (µ_r = 1)]

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/ s, respectively. The critical angle for a ray of light for these two media is ______.

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at a height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm, the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is `N/100`, where N is an integer, the value of N is ..........

A ray of light is incident at an angle of incidence of 60° on the glass slab of refractive index `sqrt3`. After refraction the light ray emerges out from other parallel faces and the lateral shift between the incident ray and emergent ray is `4/sqrt3` cm. The thickness of the glass slab is ..........

Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of air of height h = `1/3` cm, and the second and third layers are of equal thickness d = `(sqrt3 - 1)/2` cm and refractive indices μ₁ = `sqrt(3/2)` and μ₂ = `sqrt3` respectively.

A light source O is placed on the top of the first unit, as shown in the figure. A ray of light from O is incident on the second layer of the first unit at an angle of θ = 60° to the normal. For a specific value of n, the ray of light emerges from the bottom of the configuration at a distance l = `8/sqrt3` cm, as shown in the figure. The value of n is ...........