Question

# Two plane mirrors M1 and M2 are inclined at 30∘to 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 8√3 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=8√3 cm

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