#### Question

Light of wavelength 5000 Å falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

#### Solution

Wavelength of incident light, λ = 5000 Å = 5000 × 10^{−10} m

Speed of light, *c* = 3 × 10^{8} m

Frequency of incident light is given by the relation,

`v = c/lambda`

`= (3xx10^8)/(5000xx10^(-10)) = 6xx 10^14 Hz`

The wavelength and frequency of incident light is the same as that of reflected ray. Hence, the wavelength of reflected light is 5000 Å and its frequency is 6 × 10^{14} Hz.

When reflected ray is normal to incident ray, the sum of the angle of incidence, `anglei` and angle of reflection, `angler` is 90°.

According to the law of reflection, the angle of incidence is always equal to the angle of reflection. Hence, we can write the sum as:

`anglei + angler = 90`

`anglei + anglei = 90`

`anglei = 90/2 = 45^@`

Therefore, the angle of incidence for the given condition is 45°.