Question

the focal length of a concave mirror is 7 cm. the image is formed 5 cm behind the mirror. find the distance of the object from the mirror. ​

Answer 1

Given:

Focal length(f) = 7 cm.

Distance of the image(v) = -5 cm

To find:

The distance of the object from the mirror(u).

Solution:

Focal length of the mirror(f) = 7 cm.

The image is formed 5 cm behind the mirror.

So, the distance of the image (v) = - 5 cm.

The distance of the object(u) = ?

From the formula we get that,

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

$or, \dfrac{1}{7} = [\dfrac{1}{u} + (-\dfrac{1}{5} )]$

$or, \dfrac{1}{7} = (\dfrac{1}{u} - \dfrac{1}{5} )$

$or, ( \dfrac{1}{u} - \dfrac{1}{5} ) = \dfrac{1}{7}$

$or, \dfrac{1}{u} = (\dfrac{1}{5}+\dfrac{1}{7})$

$or, \dfrac{1}{u} = (\dfrac{7+5}{35})$ [∵ The L.C.M. of the denominators is 35.]

$or, \dfrac{1}{u} = \dfrac{12}{35}$

$or, u = \dfrac{35}{12}$

or, u = 2.916

or, u = 2.92 cm

∴ The object is placed at a distance of 2.92 cm in front of the mirror.

Answer:

          The object is placed at a distance of 2.92 cm in front of the mirror.