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Question

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

A
60 cm and 30 cm
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B
30 cm and 15 cm
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C
30 cm and 60 cm
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D
15 cm and 30 cm
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Solution

The correct option is A 60 cm and 30 cm
Given:
Image formed is real, and hence, is inverted in case of concave mirror.
Image size h2 is half of object size h1 :
h2h1=12

Let image distance be v and object distance be u.
Magnification for concave mirror is given by:
m=vu=h2h1
vu=12
v=u2
Radius of curvature, R=40 cm
Focal length (f) is half the radius of curvature (R)
f=R2
f=402=20 cm
Using mirror formula,
1u+1v=1f
1u+2u=120
u=60 cm
v=u2
v=602=30 cm

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