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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
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 :-  .................... (2)
mirror equation for real image :- ........................(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

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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