Refraction physics

Question

  Light passes from diamond into air. The angle of refraction as the light emerges from the diamond is 42 degrees. The angle of incidence was___ degrees.

 

Light travelling from air into transparent material is incident at an angle of 32 degrees and refracted at an angle of 24 degrees. The index of refraction of the transparent material is ____.

 

Light of wavelength 838nm travelling through the air enters crown glass at an angle of 27.0 degrees.The wavelength of the light in the crown glass was ___nm.

 

The critical angle for a ethanol-water interface is ____ degrees

Answer 1

(a)

The Angle of the Refraction is 42°

We know that from Snell's law

n₁sin(θ_i) = n₂sin(θ_r)

sin(θ_i) = (n₂ / n₁) sin(θ_r)

The Refractive Index of air is 1.0003

The Refractive Index of Diamond is 2.42

sin(θ_i) = (1.0003 / 2.42) sin(42)

sin(θ_i) = 0.2765

(θ_i) = 16.05°

Therefore angle of Incidence is 16.05°.

Answer 2

(b)

The Angle of the Incidence is 32°

The Angle of the Refraction is 24°

We know that from Snell's law

n₁sin(θ_i) = n₂sin(θ_r)

The Refractive Index of air is 1.0003

The Refractive Index of Diamond is 2.42

1.0003 sin(32) = n₂sin(24)

n₂sin(24) = 0.53

n₂ = 1.303

Therefore Refractive Index of Transparent material is 1.30.

Answer 3

(c)

The Angle of the Incidence is 27°

We know that from Snell's law

n₁sin(θ_i) = n₂sin(θ_r)

The Refractive Index of air is 1.0003

The Refractive Index of Crown Glass is 1.52

1.0003 sin(27) = 1.52sin(θ_r)

sin(θ_r) = 0.2987

θ_r = 17.38°

Snell's law in terms of Wavelength is

λ₂sin(θ_i) = λ₁sin(θ_r)

Wavelength of light in the air is 838 nm

λ₂sin(27) = 838 * sin(17.38)

λ₂  = 551.48

Therefore Wavelength of light in Crown glass is 551.48 nm.

Answer 4

(d)

The Angle of the Refraction is 90° for Critical Angle condition

We know that from Snell's law

n₁sin(θ_c) = n₂sin(90)

n₁sin(θc) = n₂

The Refractive Index of Ethanol is 1.37

The Refractive Index of water is 1.33

sin(θ_c) = (1.33 / 1.37)

sin(θc) = 0.970

(θc) = 76.12°

Therefore Critical angle is 76.12°.