Question

focal length of a concave mirror is 8cm. The object is placed at 16 cm infront of the mirror. Write the position of image and it's nature.​

Answer 1

Given :

In concave mirror,

Focal length = - 8 cm

Object distance = - 16 cm

Note : In concave mirror focal length is negative.

To find :

The position of image and it's nature.

Solution :

using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

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

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

By substituting all the given values in the formula,

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 16} = - \dfrac{1}{8}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{ 16} = - \dfrac{1}{8}$

$\dashrightarrow\sf \dfrac{1}{v} = - \dfrac{1}{8} + \dfrac{1}{ 16}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 2 + 1}{ 16}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1}{ 16}$

$\dashrightarrow\sf v = - 16\: cm$

Thus, the position of the image is - 16 cm from the mirror.

Nature of image :

• The image is formed in front of the concave mirror, it is real and inverted