The numerical value of the focal length of a thing convergent lens is f and an object is at a distance of  u from the lens ; a plane mirror is placed behind the lens perpendicular to the axis at a distance d from the lens. The image of the object after reflection at the  mirror and a second refraction through the lens is at a distance v in front of the lens. Prove that  , u+v=2f

Asked by mridulabarua05 | 9th Feb, 2019, 01:21: PM

Expert Answer:

It is asked to prove u+v = 2f , which is independent of distance d betweem lens and mirror.
It is doubtful for getting same lens-to-image distance v, if you vary the lens-to-mirror distance d,
when object-to-mirror distance u is fixed and  focal length f of lens is constant.
 
geometrically, placing a mirror at distance d from lens and making second refraction by same lens is equivalent
to placing two convex lens of same focal length separated by distance 2d. In this case the effective focal length F  is given by
 
begin mathsize 12px style 1 over F space equals space 2 over f minus fraction numerator 2 d over denominator f squared end fraction end style
hence we get  begin mathsize 12px style 1 over v plus 1 over u space equals space 2 over f minus fraction numerator 2 d over denominator f squared end fraction end style 
 

Answered by Thiyagarajan K | 11th Feb, 2019, 08:19: PM

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