Question

Two mirrors each 1.6 m long are facing each other. The distance between the mirrors is 20 cm. A light ray is incident on one end of the mirror at an angle of incidence of ${30}^{\circ }$ . How many times is the ray reflected before it reaches the other end?

Answer 1

Given,

Distance $BC=20cm$

$ABC=CBD={30}^0$

Now,

In $△BCD$

$DC=BCtan{30}^0=20.tan{30}^0$

BC = 20cm

ABC = CBD = 30o

Now,

in triangle BCD

$DC=BCtan{30}^{=}20.tan{30}^0$

So,

$DC=\frac{20}{\sqrt{3}}cm$

thus, the ray of light undergoes one reflection for every horizontal distance of 20/√3cm. The total distance covered to make all the reflections will be,

The number of reflections will be [length of mirror = 1.6m = 160cm]

$=\frac{160}{\left(\frac{20}{\sqrt{3}}\right)}$

$\sim 14reflections$