For a certain optical medium the speed of light varies from a low value of 1.90 × 10 8 m/s for violet light to a high value of 2.00 × 10 8 m/s for red light. (a) Calculate the range of the index of refraction of the material for visible light. (b) A white light is incident on the medium from air, making an angle of 30.0° with the normal. Compare the angles of refraction for violet light and red light. (c) Repeat the previous part when the incident angle is 60.0°.

a. The refractive index ranges from 1.5 - 1.56

b. 18.7° for violet light and 19.5° for red light.

c. 33.7° for violet light and 35.3° for red light.

Explanation:

a. The refractive index of an object is the ratio of the speed of light in a vacuum and the speed of light in the object.

Mathematically,

The speed of violet light in the object is .

The speed of red light in the object is

Hence, the refractive index for violet light is:

and for red light, it is:

Hence, the refractive index ranges from 1.5 - 1.56.

b. The refractive index is also the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

The angle of incidence is 30°.

The angle of refraction for violet light will be:

And the angle of refraction for red light will be:

The angle of refraction for red light is larger than that of violet light when the angle of incidence is 30°.

c. The angle of incidence is 60°.

The angle of refraction for violet light will be:

And the angle of refraction for red light will be:

The angle of refraction for red light is still larger than that of violet light when the angle of incidence is 60°.