Question

4) The radius of curvature of a concave mirror is 20cm. It forms a real and invented image
of an object at 30cm. The object distance is
b) 10cm
c) 15cm
d) 20cm​

Answer 1

Given :

In concave mirror,

Radius of curvature = 20cm

Image distance = 30cm

To find :

The object distance

Solution :

we know that,

Focal length = Radius of curvature/2

f = 20/2

f = 10cm

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,

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

$\dashrightarrow\sf \dfrac{1}{30} + \dfrac{1}{u} = \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{u} = \dfrac{1}{10} - \dfrac{1}{30}$

$\dashrightarrow\sf \dfrac{1}{u} = \dfrac{3 - 1}{30}$

$\dashrightarrow\sf \dfrac{1}{u} = \dfrac{2}{30}$

$\dashrightarrow\sf \dfrac{1}{u} = \dfrac{1}{15}$

$\dashrightarrow \boxed{\sf u = 15 \: cm}$

The Object distance is 15cm.

Hence, option (c) 15cm is correct