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Question

An object of 5.0 cm height is placed at a distance of 20 cm in front of a concave mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

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Solution

Radius of curvature (R) = 30 cm
f=R2=302=15 cm
Focal distance for concave mirror, f=15 cm
Object distance, u=20 cm
Height of the object, ho=5 cm
According to mirror formula,
1v+1u=1f
1v=1f1u
1v=115+120=4+360=160
Image distance,v=601= 60 cm
Image is real , inverted and in front of the mirror.
m = hih0=vu
hi5=6020
hi=15 cm

Image formed is inverted as size comes out to be negative.
Image is real as it is forming in front of the mirror.
Size of image is 15 cm.

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