Please solve the question in the attached file.

Asked by hemeshsaini2005 | 26th Oct, 2021, 01:49: PM

Expert Answer:

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 begin mathsize 14px style angle end styleQRT  = begin mathsize 14px style angle end styleQSR = 90obegin mathsize 14px style angle end styleSQR = begin mathsize 14px style angle end styleSRT = e .
From figure it is seen that mirror is to be rotated by ( begin mathsize 14px style angle end styleSRT - (A/2 ) ) =  ( 4 - 2 ) = 2o
    

Answered by Thiyagarajan K | 27th Oct, 2021, 09:11: PM