Question

The index of refraction varies slightly for electromagnetic waves in a medium; this phenomena results in rainbows as white light (containing all colors) passes through water droplets in the sky. Calculate the ang le between refracted rays in a water droplet if nblue = 1.339 for blue light and nyellow = 1.330 for yellow light and a white sunlight ray strikes a water droplet 45.00 from the normal. A. 0.24 OB. 0.29° OC. 0.52 D. 0.73 OE. 1.05

Answer 1

E. 1.05

Step-by-step explanation:

Angle of incidence= 45°

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

n₁ is the refractive index for blue light which is 1.339

n₂ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{45.0}^0}=\frac {1.339}{1}`

`{sin\theta_2}=0.9408`

Angle of refraction for blue light = sin⁻¹ 0.9408 = 71.20°.

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 1.330

n₂ is the refractive index of air which is 1

So,

`\frac {sin\theta_2}{sin{45.0}^0}=\frac {1.330}{1}`

`{sin\theta_2}=0.9406`

Angle of refraction for yellow light = sin⁻¹ 0.9406 = 70.15°.

The difference in the angle of refraction = 71.2° - 70.15° = 1.05°