Question

If object is at 60 cm from concave mirror of focal length 25 cm . Find the image distance and magnification.​

Answer 1

Given :

In concave mirror,

Object distance = - 60 cm

Focal length = - 25 cm

To find :

The image distance and magnification.

Solution :

we know that ,

» 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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 60} = \dfrac{1}{ - 25}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{60} = \dfrac{1}{ - 25}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{ - 25} + \dfrac{1}{60}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 12 + 5}{300}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 7}{300}$

$\dashrightarrow\sf v = - \dfrac{300}{7}$

$\dashrightarrow\sf v = - 42.8 \: cm$

Thus, the position of image is -42.8 cm.

we know that,

» The linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign that is,

$\dashrightarrow\bf m = - \dfrac{v}{u}$

$\dashrightarrow\sf m = - \dfrac{ \dfrac{300}{7} }{6}$

$\dashrightarrow\sf m = - \dfrac{300}{6 \times 7}$

$\dashrightarrow\sf m = - \dfrac{50}{7}$

$\dashrightarrow\sf m = -7.1$

Thus, the magnification is 7.1