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# solve

we have miiror equation (1/u) + (1/v) = (1/f)  ...................(1)

where u is mirror-to-object distance ( sign -ve for concave mirror),  v is mirror-to-image distance and f is focal length ( sign -ve for concave mirror )

Initial image distance is obtained from eqn.(1) with apllying appropriate sign convention

(-2/f) + (1/v ) = (-1/f)     or v  = f  , image is formed behind the mirror, virtual

initial magnifiacation m = -v/u  = -f/(-f/2)   = 2   .................(2)

after moving the object f/4 away from mirror, image  distance is obtained from eqn.(1) :- (-4/3f) + (1/v) = (-1/f)   or  v = 3f

magnification m = -v/u  = -3f/(-3f/4)  = 4  ...................(3)

Ratio of magnifications = 4/2 = 2
Answered by Expert 10th May 2019, 12:45 PM
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