The refractive indices of water and glass are 4/3 and 3/2 respectively. Determine the refractive index of a ray of light moving from water to glass. (3mks)

Light is incident on an air-glass boundary at an angle of incidence of 40⁰. If the refractive index of the glass is 1.7, determine the angle of refraction. (3mk)

Fig (i) and (ii) show refraction of light at air-water interface. Determine angle Ø in figure (ii)

A ray of light is incident on a glass oil interface as shown in figure below. Determine the value of r (Take refractive index of glass and oil as 3/2 and 6/3 respectively)3mk

The figure below shows a ray of light traveling through water, whose refractive index is 1.33 and glass.

Determine the refractive index of glass. (3mks)

A ray of light makes a glancing angle of incidence i = 60^o with a flat glass surface as shown in figure

Given that the critical angle for glass is 42^o determine;

(i) The refractive index of glass (2mks)

(ii) The angle of refraction r (2mks)

(iii) Given that the speed of light in air 3.0 x 10⁸m/s, find the speed of light in glass (2mks)

A ray of light traveling in the direction EO in air enters a rectangular block as shown. The resulting angle of refraction is 18⁰.

Find:-

The refractive index of the block. (2mks)
The critical angle C of the block. (3mks)

A ray of light travels from air into medium 1 and 2 as shown.

Calculate;

i) The refractive index of medium 1.
Critical angle of medium 1

iii) The refractive index of medium 2 relative to medium 1 (₁n₂)

For three media with parallel boundaries as shown in figure below, show that

₂n₃ = ₂n₁ x ₁n₃ (3mk)

A ray light is incident at right angles at the face AB, of a right angled isosceles prism of refractive index 1.6 as shown in the figure below.

If the prism is surrounded by a liquid of refractive index 1.4. Determine:

The angle of incidence on the face BC. (1mk)
The angle of refraction on the face BC. (3mk)

Two glass prisms are placed together as shown in figure below:

If a beam of light strikes the face of one of the prisms normally as shown, at what angle q does the beam emerge from the prism? (5mks)

Figure below shows the path of light through a transparent material placed in air.

Calculate the refractive index of the transparent material. (3mks)

A student carried out and experiment on refraction of light incident on a glass block.

Sheobtained the following.

i	r	Sin i	Sin r
20^o	12.7^o
30^o	18.9^o
40^o	25.0^o
50^o	30.0^o
60^o	34.0^o
70^o	37.0^o

(i). Complete the table for the values of sin i and sin r. (1mk)

(ii). Draw the graph of sin i (y – axis) against sin r. (5mk)

(iii). Determine the slope of the graph. What does it represent? (4mk)

(iv). Use the results in b (iii) to calculate the velocity of light in glass, given that velocity of light in vacuum is 3.0 x 10⁸ m/s. (3mk)

SPEED OF LIGHT

Light travels through glass of refractive index 5 with a speed V. Calculate the value of V. (Speed of light in air = 3.0 x 10⁸ m/s). (2mk)

Paraffin has a greater refractive index than that of water. Comment about the relative velocity of light in paraffin and in water.
Calculate the refractive index of glass given that the velocity of light in air is 3x 10⁸ ms^-1 and velocity of light in glass is 2.4 x 10⁸ms^-1.

Calculate the speed of light in water (n_w = 4/3, C= 3 x 10⁸ms)

Liquid X has a greater refractive index than liquid L. What information does this statement give with regard to:

(i) Velocity of light in the two liquids? (1mk)

(ii) The path of light ray moving from liquid X to liquid L if the angle of incidence in X is greater than zero degrees (i.e. i° > 0⁰) (1mk)

REAL AND APPARENT DEPTH

The diagram below shows a transparent water tank containing water of refractive index 4/3. An electric light is fixed at corner A of the tank. A light ray from the slit shines on the water surface BC at an angle of 48⁰as shown

Determine the angle of refraction for the ray shown in the diagram.
Complete the diagram to show the refracted ray.

Figure shows a coin placed in a large empty container. An observer looking into the container from the position shown is unable to see the coin.

Sketch two rays from a point on the coin to show how the observer is able to

see the image of the coin after the container is filled with water.

An Eskimo walking along an Iceland observed an inverted image in the sky of a polar bear standing some distance away. Explain (2mks)

A coin is placed beneath a transparent block of thickness 10cm and refractive index 1.50. Calculate the vertical displacement of the coin. (3mks)
A ray of light is directed at an angle of 50⁰ on to a liquid-air boundary. The refractive index of the liquid is 1.4.Show on a diagram the patch taken by the ray on striking the liquid-air boundary. Show how you arrive at your answer.

A small object lies at the bottom of a water pond at a depth of 2.4m.Given that the refractive index of water is 1.3, determine the apparent depth of the object. Give your answer to 1 decimal place.

A nail at the bottom of a beaker containing glycerine appears to be 6.8 cm below the surface of glycerine. Determine the height of the glycerine in the beaker. (take the refractive index of glycerine as 47) (3mk)

A beaker of height 10 cm is filled with water. An optical pin which is at the bottom of the beaker is then viewed from the top of the beaker. How far does the pin appear from the surface, if the refractive index of water is ) (2mk)
A pin is placed horizontally at the bottom of a beaker 9cm tall completely filled with a liquid. Viewing from the top, the pin appears to be 2cm above the bottom of the beaker. Calculate the refractive index of the liquid. (3mk)

The real thickness of crown glass block of refractive index 58 is 10cm is 10cm. Calculate theapparent thickness of the glass.

A microscope is focused on a mark on a horizontal surface. A rectangular glass block 30mm thick is placed on the mark. The microscope is then adjusted 10mm upwards to bring the mark back to focus. Determine the refractive index of the glass. (3mk)

Calculate the apparent depth of an object, O in the fig (3mk)

A traveling microscope (M) is focused on a coin placed at the bottom of an empty beaker as shown in the figure below

When water of refractive index 1.33 is poured into the beaker, the microscope has to be raised through 3cm to focus the image of the coin, figure (ii). Calculate the height of water poured into the beaker (3mk)

A vertical pin is fixed at the centre of a rectangular container with thin transparent walls as shown below.

A transparent liquid is then poured into the container. When viewed from side A, the distance of the pin is 1.9cm from the edge, determine the refractive index of the liquid. (2mk)

A small bright object O lies at the bottom of a beaker containing water of depth h. A convex lens of focal length 15cm is held at the surface of the water. With this arrangement the image of O is formed at a point 45cm from the water surface as shown in the figure below.

Taking the refractive index of water to be 4/3. Determine

the apparent depth of the object (2mk)
the real depth h, of the object (3mk)

The data below shows the results obtained when such an experiment was performed by form three students using various values of real depths, Y of a liquid.

Real depth (cm)	30	50	70	90	110	130
Apparent depth(cm)	22	37	52	66	81	96

i) Plot a graph of the real depth (y-axis) against apparent depth.
ii) From the graph, determine the refractive index of the liquid.

In an experiment to determine refractive index of water, a black line is painted on the bottom of a tall glass container which is then partially filled with water. The black line appears closer than it is really. The following results were recorded from the experiment

Real depth (cm)	8.1	12	16	20
Displacement (cm)	2.2	2.9	4	4.9
Apparent depth(cm)

Complete the table for apparent depth row (2mks)

Plot a graph of real depth against apparent depth on the grid provided (5mks)

(iii) Determine the refractive index for the water (2 mks)

The table below shows results obtained when an experiment was carried out using various depths of a liquid.

Real depth (cm)	8.0	12.0	16.0	20.0	24.0	28.0
Apparent depth (cm)	4.88	7.32	9.76	12.20	14.64	17.08

(i) Use the table to plot a graph of apparent depth against real depth (5mks)

(ii) Use the graph to determine the refractive index of the liquid. (3mks)

(iii) What is the real depth of the pin when the apparent depth is 2.44cm? (2mks)

The graph shown below shows, the apparent depth (y-axis) against real depth. Use it to calculate the refractive index of glass.

TOTAL INTERNAL REFLECTION

Explain what you understand by the term critical angle as applied in optics (1 mk)

State two conditions necessary for total internal reflection to occur 2 mks

State TWO uses of total internal reflection.

Give one use of an optical fibre. (1mk)

State two uses of optical fibres whose working relies on total internal reflection.

(2mk)

Kenya launched the use of optical fibres in communication recently. State why optical fibres are preferred to ordinary cables.

A glass prism of has refractive index of 1.5. Calculate the critical angle of this glass prism (3mk)
The refractive index for air to water is , find the critical angle C for water – air interface

Critical angle of a material is 42⁰, determine the angle of retraction of light in the material if theincidence angle is 30⁰. (2 mks)

The refractive index for air-water boundary is 4/3. Calculate the critical angle for water–air interface.

Explain with an aid of a diagram why to a diver under water, most of the surface looks slivery. Bubbles of air rising from the diver look slivery. (2mk)

Explain with the aid of a diagram, how a suitable glass prism may be used to turn a ray of light 180⁰

Light travels from glass to air as shown. The refractive index of glass 1.5

(a) Determine angle x (2mk).

b). What name is given to angle x? (1mk)

The figure below shows the path of a ray of light passing through a rectangular glass block placed in air.

Calculate the refractive index of glass. (2mk)

Complete the path of the ray shown until when it leaves the glass prism, given that the criticalangle from glass is 42⁰. (Show all the angles). (n = ³/₂ for glass)

Complete the path of the ray shown until when it leaves the glass prism, given thatrefractive indexfor glass is n= 1.5 and the critical angle of glass is 42⁰. (Show all the angles). (3mk)

The figure below shows two rays of light incident normally on one face of a glass prism, whose critical angle is 42º .

Complete the diagram to show the paths of the two rays as they pass through the prism. 3mks

Two rays are incident on the base of a triangular prism whose angles areas shown in the figure below. If the refractive index is, determine the angle between the two emergent rays. (3mks)

Figure 6 show a ray of light incident on the face of a water prism.

Sketch the path of the rays as it passes through the prism. Critical angle for water is 49⁰

The fig 1 below shows a ray of light incident on a glass prism

Given that the critical angle for the grass is 39⁰, sketch on the diagram the path of the ray through the prism (2 mk)

The figure below shows two rays A and B entering a semi circular glass block which has critical angle of 42⁰. The rays are incident at an air glass boundary at point O

Complete the path of the two rays from point O. Label A¹ and B¹ the corresponding rays.

DISPERSION OF LIGHT

Other than the peeling off of the silvering on mirrors. State two other disadvantages of plane mirrors over prisms in making periscopes. ( 2mk)

What is dispersion of light? (1mk)

What measurable quantity is associated with colour of light?

Fig shows white light falling on a prism.

a) Name the colour at X and Y (1 mk)
b) Explain why a prism disperses white light into its component colours.(1 mk)

The figure below shows a ray of light passing into a glass prism ABC. Sketch the path of the ray as it travels from the face AC. (critical angle for glass is 42⁰) (2mk)

The figure below represents a ray of white light incident on one face of a triangular prism, a spectrum is observed on a screen on the other side of the prism. Draw a labeled diagram to show the path of differently coloured rays which produces the spectrum observed on the screen. (3mk)

The figure shows the path of a yellow light through a glass prism. The speed of yellow light in the prism is 88 x 10⁸ m/s.

a) Determine the refractive index of the prism material for the light. (Speed of light in vacuum = 3.0 x 10⁸ ms^-1)
b) Show on the figure, the critical angle C and determine its value.
c) Given that r= 21.2⁰, determine angle Ө

(d) Determine the critical angle for the prism. (2mk)

e) On the same figure, sketch the path of the light after striking the prism if the prism was replaced by another of similar shape but lower refractive index. (Use dotted line for your answer).

Figure shows the path of a ray of red light through a glass prism. The speed of red light in the prism is 2.02 x 10⁸m/s.

a) Determine the refractive index of glass for red light given that the speed of light in air is 3.0 x 10⁸m/s. (2 mks)
b) Calculate the wavelength of red light in air if the frequency of red light is

4.3 x 10¹⁴Hz. (2 mks)

c) Calculate the wavelength of red light in glass. (2 mks)
d) Given that the angle of refraction is 25.6⁰. Determine the value of the angle of incidence. (2 mks)
e) Draw a ray to compete the path of red light in figure above up to the point where it hits the screen. (Label this ray as e) `
f) If the red light shown in above is replaced by yellow light. Complete the entire path of yellow light until it hits the screen. (Label this ray as f) (1 mk)
g) Is the speed of yellow light in glass more or less than that of red light? Explain your answer. State one reason why prisms produce better optical instruments than plane mirrors (1mk)
A student used the set up below in order to determine the refractive index of glass white light. The results obtained are displayed in the table below the diagram

Angle i⁰	20	25	30	35	45	50	55	65	70
Angle D⁰	67	52	41	39	38	41	44	57	60

(i) In the grid below, plot a graph of D⁰ against i⁰ (5 marks

(ii) From the graph, determine the minimum angle of deviation, d⁰ (2mk)

(iii) Using the equation

Determine, n, the refractive index of the glass (2 marks)

(iv) Use your value of n in (iii) above to determine the critical angle of glass for white light (3 marks)

SCHEEM

An Eskimo walking along an Iceland observed an inverted image in the sky of a polar bear standing some distance away. Explain (2mks)

ANS

The layers of air above the ice are such that warm air is above and temperature decreases downwards. When light from the bear travels across the layers of air it is refracted downwards until total internal reflection occurs making the apparent position of the image to be in sky.

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