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A real image of half the size is obtaine...

A real image of half the size is obtained in a concave spherical mirror with a radius of curvature of 40 cm. The distance of object and its image will be

A

60 сm and 30 cm

B

30 cm and 60 cm

C

15 cm and 30 cm

D

30 cm and 15 cm

Text Solution

Verified by Experts

The correct Answer is:
B
Radius of curvature, R = 40 cm
Focal length, ` f = R/2 = 40/2 = 20cm`
magnification =`1/2`
`m = v/u = 1/2 rArr u = 2v`
`1/f = 1/v + 1/u rArr - 1/20 = 1/v + (1)/(2v) rArr - 1/20 = (2+1)/(2v)`
`rArr - 1/20 = (3)/(2v) rArr v = -30cm`
`u = 2 xx (-30) = -60 cm`
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