Question

A person stand straight in front of a convex mirror at a distance of 30m away from it .He sees his erect image whose height is 1÷6th real height .Find focal length of the convex mirror

Answer 1

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Answer 2

Answer:

The focal length of the convex mirror is 6 m.

Explanation:

Given that,

Distance of the object u = -30 m

Height of image $h'=\dfrac{h}{6}$

We know that,

The magnification is

$m=-\dfrac{v}{u}=\dfrac{h'}{h}$

$-\dfrac{v}{-30}=\dfrac{\dfrac{h}{6}}{h}$

$\dfrac{v}{30}=\dfrac{1}{6}$

$v = 5\ m$

Using mirror's formula

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

$\dfrac{1}{f}=\dfrac{1}{-30}+\dfrac{1}{5}$

$\dfrac{1}{f}=\dfrac{1}{6}$

$f = 6\ m$

Hence, The focal length of the convex mirror is 6 m.