Angle of deviation and calculation; real and apparent depth

REFRACTION THROUGH TRIANGULAR AND RECTANGULAR PRISM

• Triangular prism
• Rectangular prism
• Angle of deviation
• Real and apparent depth

Triangular prism

When a ray of light passes through a triangular prism, it is refracted as shown below

Angle of deviation

The angle between the incident ray and the emergent ray is known as the angle of deviation. The angle of deviation decreases as the angle of incidence increases

The refractive index, n=sin (A/2+D/2)/sin A/2

Rectangular prism

Real and apparent depth

A thick slab of glass appears to be only two –third of its real thickness when viewed vertically from above. Similarly, water in a pond appears to be only three quarters of its real depth. Rays from a coin at the bottom of a bucket of water are refracted away when they leave water and enter the eyes. They appear as if coming from a virtual image, which is apparent depth while the actual depth of the bottom remains and is referred to as real depth

Refractive index=real depth/apparent depth

CLASSWORK 1

1. Define the refraction of a medium
2. A ray of light is incident on an angle of 30⁰ on a glass prism of refractive index 1.5. Calculate the angle through which the ray is minimally deviated in the prism. (The medium surrounding the glass is air)

ASSIGNMENT 1

SECTION A

1. A transparent rectangular block 3.0cm thick is placed on the letter A written on a white cardboard. When the letter was viewed from the top of the glass block, it appeared to be 2cm. calculate the refractive index of the block (a) 3/2 (b) 5/3 (c) 1/2 (d) 3/2
2. The velocities of light in air and glass are 3.0 x10⁸ m/s and 1.8 x10⁸ m/s respectively. Calculate the sine of the angle of incidence that will produce an angle of refraction of 30⁰ for a ray of light incident on glass A 1.2 B 1.0  C 0.8  D 0.6
3. A transparent rectangular block 5.0 cm thick is placed on a black dot. The dot when viewed from above is seen 3.0 cm from the top of the block. Calculate the refractive index of the material of the block A 2/5 B 3/5 C 3/2 D 5/3 E 5/2
4. The horizontal floor of a water reservoir appears to be 1.0m deep when viewed vertically from above. If the refractive index of water is 1.35, calculate the real depth of the reservoir (a) 2.35m (b) 1.35m (c) 1.00m (d) 0.35m
5. A beam of light travelling through air at 3.0×10⁸m/s enters a pool of water of refractive index 4/3, what is its speed as it travels through water (a) 2.25×10⁸ms^-1 (b) 3.25×10⁸ms^-1 (c) 4.25×10⁸ms^-1 (d) 5.25×10⁸ms^-1
6. The absolute refractive indexes of glass and water are 3/2 and 4/3 respectively. The refractive index at the interface when a ray travels from water to glass is A ½ B 8/9 C 9/8 D17/12

Use the information below to answer questions 7, 8 and 9

The angle of incidence of a narrow beam of light on a side of an equilateral triangular prism is 48⁰. Calculate the:

7. Angle of minimum deviation (a) 36⁰ (b) 30⁰ (c) 45⁰ (d) 60⁰
8. Angle of refraction (a) 36⁰ (b) 30⁰ (c) 45⁰ (d) 60⁰
9. Refractive index of the material of the prism (a) 1.50 (b) 1.26 (c) 0.55 (d) 2.0
10. A ray of light is incident normally on an air-glass interface. What is its angle of refraction? (a) 90⁰ (b) 60⁰ (c) 30⁰ (d) 0⁰

SECTION B

1. State the laws of refraction of light
2. A triangular glass prism of thickness 10cm is placed on a dot on a piece of paper resting on a horizontal bench. (a) Draw a ray diagram to show the apparent position of the mark in the glass prism. (b) Calculate the apparent displacement of the mark, if the refractive index of the material of the prism is 1.5
3. A ray experiences minimum deviation 40⁰ when passing symmetrically through an equilateral glass prism. Calculate the angle of incidence of the ray (refractive index of glass = 1.5)