Question

An object is placed to the left of a convex mirror, such that the object-to-image distance is 88 cm.

Find the focal length of the mirror, if the image is 20 cm from the mirror.

Answer 1

Ans

The focal length of mirror = 28.333 cm

Explanation

Let d_o = Object distance from the mirror

d_i = Image distance from the mirror

As d_i = 20 cm

d_o + d_i = 88 cm

Thus d_o = 88 - 20 = 68 cm

Now object is on left side of mirror thus position of object u = - 68 cm

Position of image v = 20 cm

Let f be focal length of convex mirror thus using mirror formula we have

$\frac{1}{v} \ + \ \frac{1}{u} = \frac{1}{f}$

$\frac{1}{20} \ - \ \frac{1}{68} = \frac{1}{f}$

$\frac{68 \ - \ 20}{20 \times 68} = \frac{1}{f}$

$\frac{48}{1360} = \frac{1}{f}$

$f = \frac{1360}{48}$

f = 28.3333 cm

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