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Asked by hemeshsaini2005 | 26 Oct, 2021, 01:49: PM
If the light ray retraces its path after reflection means , mirror is oriented normal to the emergent ray from prism.

Incident light ray is horizontal . if angle of prism is A , then angle of incidence of light ray is A/2

angle of refraction r1 at the incident surface of prism is determined by law of refraction

sin(A/2)  / sin(r1)  = 1.5      or  sin(r1 )  = sin(2) / 1.5 = 0.023    , hence r1 = 1.33o

Let r2 be the angle of incidence at emergent surface of prism .

In a prism , we have ,  A  = r1 + r2   , hence  we get  r2 = A - r1 = 4 - 1.33 = 2.67o

Angle of emergence e is determined by law of refraction

sin ( e ) / sin (r2 ) = 1.5   , sin (e ) = 1.5  sin 2.67 = 4o

Now let us position the mirror normal to emergent ray . Then light ray retraces its path
Let us extend the normal to the light emerging surface of prism to mirror as shown in figure as the line QT.
Let the light ray incident on mirror at R . From R , let us draw line RS that is parallel to light emerging surface of prism.

Since QRT  = QSR = 90oSQR = SRT = e .
From figure it is seen that mirror is to be rotated by ( SRT - (A/2 ) ) =  ( 4 - 2 ) = 2o

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