Two parallel plane mirrors $M_{1}$ and $M_{2}$ have a length of $20 m$ each and are $10 c m$ apart A ray of light is incident on one end of mirror $M_{2}$ at an angle of $53^{o}$ Calculate the number of times the ray undergoes reflections
(i) If last reflation is at the other edge of mirror.
(ii) before it reaches the other end. ${g i v e n : {t a n 53}^{*} = \frac{4}{3}}$

Open in App

Solution

$tan 53 ° = \frac{x}{10 c m} \frac{4}{3} = \frac{x}{10 c m} ∴ x = \frac{40}{3} c m$
One reflection on $M_{2}$ results into $2 x$ displacement in horizontal direction of light.
Let no of reflection on $M_{2}$ be $n$ , then
$n \times 2 x \leq 2000 c m$
or, $n \leq \frac{2000}{2 \times \frac{40}{3}} n \leq \frac{2000 \times 3}{2 \times 40} n \leq 75$
$∴$ no of reflection before it reaches the other end $= 75 + 75 = 150$ and it last reflection is at the other edge of mirror $= 76 + 75 = 151$

Suggest Corrections

Similar questions

Q. Two plane mirrors

M_{1}

and

M_{2}

each have length

1 m

and are separated by

1 c m

. A ray of light is incident on one end of mirror

M_{1}

at angle

45^{\circ}

. How many reflections the ray will have before going from the other end?

The plane mirrors $M_{1}$ and $M_{2}$ are inclined to each other such that a ray of light incident on mirror $M_{1}$ and parallel to the mirror $M_{2}$ is reflected from mirror $M_{2}$ parallel to the mirror $M_{1}$ . The angle between the two mirror is (in degrees)