Question

A convex mirror is used as a safety in a shop. It hasa focal length of 15 m. A person is standing 12m away from this mirror. Find the position of his image.

Answer 1

Given :

In Convex mirror,

Focal length = 15m.

Image distance = 12m.

To find :

The position of the image

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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 12} = \dfrac{1}{15}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{12} = \dfrac{1}{15}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{15} + \dfrac{1}{12}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{4 + 5}{60}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{9}{60}$

$\dashrightarrow\sf v = \dfrac{60}{9}$

$\dashrightarrow\sf v = 6.66 \: m$

Thus, the position of image is 6.66 m.