Light of wavelength $5000 \,\mathring{A}$ 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?

(N/A) Wavelength of incident light,$\lambda = 5000 \,\mathring{A} = 5000 \times 10^{-10} \,m$.
Speed of light,$c = 3 \times 10^{8} \,m/s$.
Frequency of incident light is given by the relation,$v = \frac{c}{\lambda}$.
$v = \frac{3 \times 10^{8}}{5000 \times 10^{-10}} = 6 \times 10^{14} \,Hz$.
The wavelength and frequency of reflected light remain the same as that of the incident light.
Hence,the wavelength of reflected light is $5000 \,\mathring{A}$ and its frequency is $6 \times 10^{14} \,Hz$.
When the reflected ray is normal to the incident ray,the sum of the angle of incidence,$\angle i$,and the 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,i.e.,$\angle i = \angle r$.
Therefore,$\angle i + \angle i = 90^{\circ} \implies 2\angle i = 90^{\circ} \implies \angle i = 45^{\circ}$.
The angle of incidence for the given condition is $45^{\circ}$.