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Question

Two plane mirrors M1 and M2 are inclined at 30to the vertical. A point object (O) is placed symmetrically between them at a distance of 4 cm from each mirror. Find the distance of the object from the second image formed in mirror M1.


A
83 cm
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B
43 cm
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C
82 cm
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D
8 cm
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Solution

The correct option is A 83 cm

From ΔOPC, sin30=4OC
OC=8 cm

Here:

I11 1st image formed on mirror M1 considering an object O.

I21 1st image formed on mirror M2 considering an object O.

I121 2nd image formed on mirror M1 considering an object I21 (Image formed by M2 of object O)

Also, we can see that I121CO is isosceles.
(ΔOCQ is congurent to ΔQCI21and CI121=CI21=OC)
OI121C=30

Using sine rule in I121CO,

xsin120=OCsin30

x=OC×3=83 cm

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