Question

Help would be appreciated

Answer 1

• 1. 37º

• 2. 39º

• 3. 31º

• 4. 2.01 × 10⁸m/s

• 5. 1.31

Step-by-step 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 sinθ₂

• sinθ₂ = sin65º/1.5 = 0.604

• θ₂ = 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 sinθ₂

• sinθ₁ = 1.5 × sin(25º)

• sinθ₁ = 0.6339

• θ₁ = 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 sinθ₂

• 1.33 × sin (23º) = 1 × sinθ₂

• sinθ₂ = 1.33 × 0.3907

• sinθ₂ = 0.51967

• θ₂ = 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