Question

Two long plane mirrors OA and OB are kept such that their reflecting surfaces are at an
angle of 60° with each other. An object P is kept in front of them such that the angle OP
makes with OA is thrice the angle that OP makes with OB. Which of the following is
correct:
A) Total 5 distinct images will be formed
B) Total 6 distinct images will be formed
C) All the images formed and the object will lie on a regular convex polygon with O as
its cente
D) The ratio of length of any two adjacent sides of the polygon on which the object and
all its images lie will be (1+13)​

Answer 1

Answer:

(A)Total 5 distinct images will be formed

Explanation:

Given that,

Two long plane mirrors OA and OB are kept such that their reflecting surfaces are at an

angle of 60° with each other.

Therefore θ=60°

Also given that,

An object P is kept in front of them such that the angle OP

makes with OA is thrice the angle that OP makes with OB.

To find no.of images(m) In between two plane mirrors inclined at certain angle we use the following relation

$m = n - 1 = \frac{360}{θ} - 1 \\ = \frac{360}{60} - 1 = 6 - 1 = 5$

Therefore,there are 5 distinct images formed and they always lie on a circle centered at O.

Hence option(A) is correct

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