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Explanation:

Question 1

1. Data:

a) Angle of incidence, θ₁ = 65º

b) Refractive index of glass,  η₂ = 1.5

c) Angle of refraction, θ₂ = ?

2. Physical principles and formulae:

The refractive index for air is taken as η₁ = 1.

The refractive index is related to the angles of incidence and refraction by Snell's law of refraction:

3. Solution:

You can substitute and solve for θ₂:

Question 2

1. Data:

a) Angle of incidence in glass, θ₂ = 25º

b) Refractive index of glass, η₂ = 1.5

c) Angle of refraction, θ₁  = ?

2. Physical principles and formulae:

This time the ray passes from the solid glass to the air. Yet, Snell's law of refraction is used by the unknown is θ₁  instead of θ₂.

3. Solution:

Question 3

1. Data:

a) Angle of incidence, θ₁ = 23º

b) Refractive index of water, η₁ = 1.33

c) Angle of refraaction in air, θ₂ = ?

2. Physical principles and formula:

Use Snell's law, η₁ sinθ₁ = η₂ sinθ₂.

3. Solution:

Question 4

1. Data:

a) Refractive index of acrylic glass, η = 1.49

b) Speed of light in air, c  = 3 × 10⁸ m/s

c) Speed of light in acrylic glass, v

2. Physical principles and formulae:

As per definition, the refractive index is the ratio of the speed of light in vacuum to the speed of light in a medium.

The speed of light in air is usually approximated to the speed of light in vacumm.

Thus the formula is:

3. Solution:

Solve for v, substitute and compute:

Question 5

1. Data:

a) Angle of incidence, θ₁ = 25.5º

b) Angle of refraction, θ₂ = 25.9º

c) Refractive index of liquid water, η₁ = 1.33

d) Refractive index of ice, η₂ = ?

2. Physical principles and formula:

3. Solution:

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