Question

An object 20 cm high is placed at a distance of 16 cm from a concave mirror which produces a real image 3 cm high what is the focal length of the mirror and position of if image

Answer 1

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Position of object = u = - 16 cm

Height of object = h = 20 cm

Height of image = h' = - 3 cm

Focal length = f = ?

Position of image = v = ?

We will use the magnification formula,

$\boxed{ \boxed{m = \frac{ - v}{u} = \frac{h_i}{h_o} }}$

- v/u = h'/h

=> - v / - 16 = - 3 / 20

=> v = - 3/20 × 16

=> v = - 2.4 cm

Now,

For finding focal length, we will use mirror formula,

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

1/ - 2.4 + 1/ -16 = 1/f

=> 1/f = - 10/24 - 1/16

=> 1/f = ( - 20 - 3)/ 48

=> 1/f = - 23/48

=> f = - 48/23

=> f = - 2.086 cm

HOPE IT HELPS

Answer 2

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