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CBSE Class 11-science Answered

A real image 2 times the size of an object is formed by a concave mirror.  When the mirror and the object are shifted,  the image formed becomes 4 times the size of the object. Find the focal length of the mirror if the image were to be shifted 24cm
Asked by bukokaakinsola39 | 31 May, 2019, 08:56: AM
answered-by-expert Expert Answer
if magnification is 2, then we have 2 = | v1 / u1 |   or  u1 =  v1 / 2  , where v1 is mirror-to-image distance
and u1 is  object-to-mirror distance.
 
hence by mirror equation, we have  ( 1/v1 ) + ( 1/u1) = 1/f   or  ( 1/v1 ) + ( 2/v1) =  3/v1 = 1/f   or v1 = 3f ....................(2)
 
where f is focal length of mirror
 
Similarly in second case, if magnification is 4, then we have 2 = | v2 / u2 |   or  u2 =  v2 / 2
 
and   ( 1/v2 ) + ( 4 / v2 ) =  5/v2 = 1/f   or v2 = 5f ....................(3)
 
Hence shift in image , v2 - v1 = 5f-3f = 2f = 24 cm  or   f = 12 cm
Answered by Thiyagarajan K | 31 May, 2019, 09:41: AM
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