Question

The position and size of the image formed whenAn object of size 1 cm is placed at a distance of 15 cm from a concave mirror of focal length 10 cm is

Answer 1

Image will be formed 30 cm in front of mirror and its size is twice as that of object and inverted

Explanation:

• Mirror formula is the relation between focal length of mirror, object distance from the mirror and image distance from the mirror
• Concave mirror is a converging mirror hence have negative focal length

Given, object distance = -15 cm

focal length of concave mirror = -10 cm

size of object h₁= 1 cm

we can find the image distance by using mirror formula, given as follows

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

where, u = object distance

v = image distance

f = focal length of mirror

=> $\frac{1}{-10} =\frac{1}{-15} +\frac{1}{v}$

=> $\frac{1}{v} =\frac{1}{15} +\frac{1}{-10}$

=> $\frac{1}{v} =\frac{2-3}{30}$

=> $\frac{1}{v} =\frac{-1}{30}$

=> v = -30 cm

By using magnification formula

$m=\frac{h_{2} }{h_{1} } =-\frac{v}{u}$

=> where h₂ = size of image

=> $\frac{h_{2} }1 } =-\frac{-30}{-15}$

=> h₂ = -2 cm

image formed is real and inverted

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