Question

A 1 cm long flame is placed at a distance of 1.5 m from a wall.How far from the wall should a CONCAVE MIRROR be placed in order to obtain a 2 cm long flame on the same wall?what is the focal length of the mirror.

Answer 1

the focal length of the mirror between 3.0 CM

Answer 2

Answer: The focal length is -1 m and the distance of the image is -3 m.

Explanation:

Given that,

Height of object h = 1 cm

Height of image h' = -2 cm

Distance of the object u = -1.5 m

Using formula of magnification

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

$\dfrac{-2}{1}=\dfrac{-v}{-1.5}$

$v = -3m$

Using mirror's formula

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

$\dfrac{1}{f}=\dfrac{1}{-3}+\dfrac{1}{-1.5}$

$f = -1 m$

Hence, The focal length is -1 m and the distance of the image is -3 m.