Answer:
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:
- sinθ₂ = sin65º/1.5 = 0.604
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:
- 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:
- 1.33 × sin (23º) = 1 × sinθ₂
- 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:
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:
- 1.33 × sin(25.5º) = η₂ sin(25.9º)
- η₂ = 1.33 × 0.4305 / 0.4368 = 1.31
