# Light of wavelength 5000 Å falls on a plane reflecting surface.

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 × 108 m

Frequency of incident light is given by the relation,

$v=\frac{c}{\lambda}$

$=\frac{3 \times 10^{8}}{5000 \times 10^{-10}}=6 \times 10^{14} \mathrm{~Hz}$

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 × 1014 Hz.

When reflected ray is normal to incident ray, the sum of the angle of incidence, $\angle i$ and angle of reflection, $\angle r$ is $90^{\circ}$.

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:

$\angle i+\angle r=90$

$\angle i+\angle i=90$

$\angle i=\frac{90}{2}=45^{\circ}$

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