Question

The index of refraction for red light in water is 1.331 and that for blue light is 1.340. A ray of white light enters the water at an angle of incidence of 78.9°. (a) What is the underwater angle of refraction for the red component of the light?

(b) What is the underwater angle of refraction for the blue component of the light? (Give your answer to three significant figures.)

Answer 1

(a) 47.08°

(b) 47.50°

Step-by-step explanation:

Angle of incidence = 78.9°

For blue 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

n₂ is the refractive index for blue light which is 1.340

n₁ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{78.9}^0}=\frac {1}{1.340}`

`{sin\theta_2}=0.7323`

Angle of refraction for blue light = sin⁻¹ 0.7323 = 47.08°.

For red 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

n₂ is the refractive index for red light which is 1.331

n₁ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{78.9}^0}=\frac {1}{1.331}`

`{sin\theta_2}=0.7373`

Angle of refraction for red light = sin⁻¹ 0.7373 = 47.50°.