Question

A concave mirror has a focal length 20 cm. A rod of length 4 cm is placed along the principal axis of mirror in such a way that the end closer to mirror lies on its centre of curvature. The length of image of rod is 55/4cm 45/4cm 35/4cm 20/6 cm

Answer 1

Given:

Focal length of concave mirror = -20 $cm$

Rod of length = 4 $cm$

To Find:

length of image of rod = ?

Solution:

Since the closer end of rod to mirror lie on centre of curvature

Radius of curvature r = 2f = -40 $cm$

So distance of the object (u)= 40 + 4 = 44$cm$

As we know from the mirror formula

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

$\dfrac{-1}{20} = \dfrac{-1}{44} + \dfrac{1}{v}$

$\dfrac{1}{v} = \dfrac{-6}{220}$

$v = - \dfrac{220}{6}$

For length of image = we take difference between r and v

Length of image = 40- 220/6

$= \dfrac{22}{6} cm$

Option iv is the solution of that question