Question

A beam of white light is incident on the surface of a diamond at an angle θa. (Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. For example, the indices of refraction in diamond are nred=2.410 for red light and nblue=2.450 for blue light. Thus, blue light and red light are refracted at different angles inside the diamond, as shown in the picture. The surrounding air has nair=1.000. Note that the angles in the figure are not to scale. Part A Now consider θc, the angle at which the blue refracted ray hits the bottom surface of the diamond. If θc is larger than the critical angle θcrit, the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find θcrit. Express your answer in degrees to four significant figures

Answer 1

Answer:

The answer is θcrit = 24.1°

Explanation:

The equation to calculate the critical angle of the refractive index of the diamond in blue light is equal to:

θcrit = sin^-1(1/nblue), where

nblue = is the refractive index of blue light = 2.45

θcrit = sin^-1(1/2.45) = 24.1°

Answer 2

Answer:

 θ (critical)= 24.089

Following is given the solution for the question stated:

Explanation:

We know that:

$θ(critical) = sin^-1 (1/n)$

As,

n = refractive index of blue light

So by putting value of n = 2.45 we get:

$θ (critical)= sin^-1( 1/2.45)$

By calculating we get:

 θ (critical)= 24.089

I hope it will help you a lot!