Question

A concave mirror forms an image of 20 cm high object on a screen placed 5.0 m away from the mirror. The height of the image is 50 cm. Find the focal length of the mirror and the distance between the mirror and the object.

 

Answer 1

Given,
Height of the object, h₁ = 20 cm,
Distance of image from screen v = −5.0 m = −500 cm,

\[- \frac{v}{u} = \frac{h_2}{h_1}\] 

\[or  \frac{- ( - 500)}{u} = \frac{50}{20}\]
Where 'u' is the distance of object from screen.
(As the image is inverted)
Using mirror formula,

\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\] 

\[or  \frac{1}{- 5} + \frac{1}{- 2} = \frac{1}{f}\]

\[or   - \frac{1}{f} = \frac{7}{10}\] 

\[or  f =  - \frac{10}{7} =  - 1 . 44  \text{ m }\]
Hence, the required focal length of the concave mirror is 1.44 m.