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1. 37º2. 39º3. 31º4. 2.01  × 10⁸m/s5. 1.31

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:

η₁ sinθ₁ = η₂ sinθ₂

3. Solution:

You can substitute and solve for θ₂:

1 × sin65º = 1.5 sinθ₂sinθ₂ = sin65º/1.5 = 0.604θ₂ = arcsin(0.604) ≈ 37º

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.

η₁ sinθ₁ = η₂ sinθ₂

3. Solution:

1 × sinθ₁ = 1.5 sinθ₂sinθ₁ = 1.5 × sin(25º)sinθ₁ = 0.6339θ₁ = arcsin(0.6339) ≈ 39º

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:

η₁ sinθ₁ = η₂ sinθ₂1.33 × sin (23º) = 1 × sinθ₂sinθ₂ = 1.33 × 0.3907sinθ₂ = 0.51967θ₂ = arcsin(0.51967) = 31º

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:

η = c/v

3. Solution:

Solve for v, substitute and compute:

v = c/η = 3×10⁸m/s / 1.49 = 2.01  × 10⁸m/s

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:

Snell's law: η₁ sinθ₁ = η₂ sinθ₂

3. Solution:

η₁ sinθ₁ = η₂ sinθ₂ 1.33 × sin(25.5º) = η₂ sin(25.9º)η₂ = 1.33 × 0.4305 / 0.4368 = 1.31

Multiply the 3 dimensions, assuming it is a rectangular cuboid, to get the volume in cm³ divide mass by volume to get density in g/cm³

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