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?

Answer 1

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

Speed of light, c = 3 × 10⁸ m

Frequency of incident light is given by the relation,

`"v" = "c"/lambda`

= `(3 xx 10^8)/(5000 xx 10^(-10))`

= 6 × 10¹⁴ Hz

The wavelength and frequency of incident light is the same as that of the reflected ray. Hence, the wavelength of reflected light is 5000 Å and its frequency is 6 × 10¹⁴ Hz.

When a reflected ray is normal to incident ray, the sum of the angle of incidence, `angle"i"` and angle of reflection, `angle"r"` 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:

`angle"i" + angle"r" = 90`

`angle"i" + angle"i" = 90`

`angle"i" = 90/2` = 45°

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