Question

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

Answer:

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

h

h

′

=

u

−v

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

1

−2

=

−1.5

−v

v = -3mv=−3m

Using mirror's formula

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

f

1

=

v

1

+

u

1

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

f

1

=

−3

1

+

−1.5

1

f = -1 mf=−1m

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