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CBSE Class 12-science Answered

A concave mirror produces a real image and the virtual image of the same magnification at distance of 0.12 m and 0.08 m respectively. The radius of curvature of mirror is
Asked by viharikashankar | 18 Jun, 2019, 10:42: PM
answered-by-expert Expert Answer
Virtual image is produced at 0.08 m (behind the mirror ) and real image is produced at 0.12 m (in front of mirror).
 
Let u1 be the object-to-mirror distance for virtual image and u2 be the object-to-mirror distance for real image.
 
since magnification is same for both the cases, we have,   .08/u1 = 0.12/u2   or    ( u1 / u2 ) = 2/3  ...................(1)
 
Let f be the focal length of concave mirror
 
mirror equation for virtual image :-  begin mathsize 14px style fraction numerator negative 1 over denominator 0.08 end fraction space plus space 1 over u subscript 1 space equals space 1 over f end style .................... (2)
mirror equation for real image :- begin mathsize 14px style fraction numerator 1 over denominator 0.12 end fraction space plus space 1 over u subscript 2 space equals fraction numerator begin display style 1 end style over denominator begin display style 0.12 end style end fraction space plus space fraction numerator begin display style bevelled 2 over 3 end style over denominator begin display style u subscript 1 end style end fraction space equals space 1 over f space end style ........................(3)
In eqn.(3), we substituted for u2 from eqn.(1)
 
Since RHS of eqn.(2) and (3) are same, we equate both LHS of eqn.(2) and (3) and solve the formed equation to get u1
 
begin mathsize 14px style fraction numerator negative 1 over denominator 0.08 end fraction plus 1 over u subscript 1 space equals space fraction numerator 1 over denominator 0.12 end fraction plus fraction numerator begin display style bevelled 2 over 3 end style over denominator u subscript 1 end fraction end style    or    u1 = 0.016 m  
Hence u2 = (3/2)u1 = (3/2)×0.016 = 0.024 m
 
By substituting u1 or u2  in eqn.(2) or (3), we get f = 0.02 m.
 
Hence radius of curvature of mirror = 0.04 m
Answered by Thiyagarajan K | 19 Jun, 2019, 04:37: PM
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