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A light ray is incident on a horizontal ...

A light ray is incident on a horizontal plane mirror at an angle of `45^(@)` . At what angle should a second plane mirror be placed in order that the reflected ray finally be reflected horizontally from the second mirror, as shown in figure

A

`theta = 30^(@)`

B

`theta = 24^(@)`

C

`theta = 22.5^(@)`

D

`theta = 67.5^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
From figure, CD = emergent ray is parallel to PQ and BC is a line intersecting these parallel lines.
So, `angle DCB + angle CBQ = 180^(@)`
`angle DCN + angle NCB + angle CBQ = 180^(@)`
`alpha + alpha + 45^(@) = 180^(@)`
`alpha = 67.5^(@)`
but `angle NCS = 90^(@)`
So, second mirror is at an angle of `90^(@) - 67.5^(@) = 22.5^(@)` with horizontal.
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