Question

Sunlight strikes a piece of crown glass at an angle of incidence of 38.0°. Calculate the difference in the angle of refraction between a yellow (580 nm) and a green (550 nm) ray within the glass. The index of refraction is n=1.523 for yellow and n=1.526 for green light. B.) The ray now travels inside the glass. What is the minimum angle of incidence at which the yellow ray can hit the surface of the glass and become there totally internally reflected and not refracted?

Answer 1

Difference in the angle of refraction = 0.3°

41.04° is the minimum angle of incidence.

Step-by-step explanation:

Angle of incidence = 38.0°

For yellow light :

Using Snell's law as:

`\frac {sin\theta_2}{sin\theta_1}=\frac {n_1}{n_2}`

Where,

Θ₁ is the angle of incidence

Θ₂ is the angle of refraction

n₁ is the refractive index for yellow light which is 1.523

n₂ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{38.0}^0}=\frac {1.523}{1}`

`{sin\theta_2}=0.9377`

Angle of refraction for yellow light = sin⁻¹ 0.9377 = 69.67°.

For green light :

Using Snell's law as:

`\frac {sin\theta_2}{sin\theta_1}=\frac {n_1}{n_2}`

Where,

Θ₁ is the angle of incidence

Θ₂ is the angle of refraction

n₁ is the refractive index for green light which is 1.526

n₂ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{38.0}^0}=\frac {1.526}{1}`

`{sin\theta_2}=0.9395`

Angle of refraction for green light = sin⁻¹ 0.9395 = 69.97°.

The difference in the angle of refraction = 69.97° - 69.67° = 0.3°

Calculation of the critical angle for the yellow light for the total internal reflection to occur :

The formula for the critical angle is:

`{sin\theta_(critical)}=\frac {n_r}{n_i}`

Where,

`{\theta_(critical)}` is the critical angle

`n_r` is the refractive index of the refractive medium.

`n_i` is the refractive index of the incident medium.

n₁ is the refractive index for yellow light which is 1.523 (incident medium)

n₂ is the refractive index of air which is 1 (refractive medium)

Applying in the formula as:

`{sin\theta_(critical)}=\frac {1}{1.523}`

The critical angle is = sin⁻¹ 0.6566 = 41.04°