Question

How far from a lamp must a concave mirror of focal length 3 cm be placed to throw it's image on screen 8cm from the lamp?

Answer 1

How far from a lamp must a concave mirror of focal length 3 cm be placed to throw it's image on screen 8cm from the lamp?

Good question,

Here is your perfect answer!

Here f = - 3cm,

v = - 8cm

(sign convention)

Applying mirror formula,

=) 1/u = 1/f - 1/v

=) 1/u = - 1/3 - (-1/8)

=) 1/u = - 1/3 + 1/8

=) 1/u = - 5/24

=) u = - 24/5 cm

=) u = - 4.8cm.

Answer 2

We know, The mirror equation,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$........................(1)

Here the mirror taken is a concave mirror.

Here:  

v = mirror to image distance = 8 m

u = mirror to object distance = ?

f = focal length = 3 m

Put the values in the equation:

$\frac{1}{8} + \frac{1}{u} = \frac{1}{3} ........................(2)$

(or) $\frac{u + 8}{8u} = \frac{1}{3}$

(or) 3u + 24 = 8u  

(or) 5u = 24

Hence, u = 4.8 m