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Question
To obtain a magnification of +2 with a concave mirror of radius of curvature 60 cm the object distance must be ______.
Options
-90 cm
-45 cm
-30 cm
-15 cm
Solution
To obtain a magnification of +2 with a concave mirror of radius of curvature 60 cm the object distance must be -15 cm .
Explanation:
Given the magnification +2.0 of a concave mirror of radius of curvature 60.0 cm .
Focal length =` 60/2` = -30
(-ve is taken because the focus of the mirror is behind the pole.)
Magnification, m`= (-v)/u`
Putting the value of magnification in the above formula we get,
`(-v)/u=2`
`v= -2u`
`v` is image distance ,`u` is object distance and `f` is focal length.
Since,
`1/u + 1/v =1/f`
Putting te values
`1/u + 1/(-2u) =1/(-30)`
`1/(2u) = 1/(-30)`
`u = -30/2cm`
`u =-15 cm`
Hence, the object distance is -15 cm.
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