Question

An object of height 6 cm is placed at 15 cm in front of a concave mirror of focal length 5cm .At what distance from the mirror should a screen be placed so that we can get a sharp and clear image?​

Answer 1

Given:

Concave mirror

• Object height = h = 6 cm
• Object pole distance = u = -15 cm
• Focal length = f = -5 cm

To find:

• Image distance = v = ?

Solution:

Applying mirror formula,

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

$\implies \sf{ \dfrac{1}{v} = \dfrac{1}{ - 5} - \dfrac{1}{ (- 15)} }$

$\implies \sf{ \dfrac{1}{v} = \dfrac{1}{ - 5} + \dfrac{1}{15} }$

$\implies \sf{ \dfrac{1}{v} = \dfrac{1}{15} - \dfrac{1}{5} }$

$\implies \sf{ \dfrac{1}{v} = \dfrac{1 - 3}{15} }$

$\implies \sf{ \dfrac{1}{v} = \dfrac{ - 2}{15} }$

$\implies \sf{v = \dfrac{ - 15}{2} }$

So, the mirror should be placed at a distance of -7.5 cm to obtain a clear and sharp image.