Question

Find the image distance and size of the image if object of height 8 cm is placed at distance of 40 cm in front of concave mirror with focal length 10 cm.​

Answer 1

Given :

In concave mirror,

Object height = 8 cm

Object distance = - 40 cm

Focal length = 10 cm

To find :

The image distance and size 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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 40} = \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{ 40} = \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{10} + \dfrac{1}{ 40}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{4 + 1}{ 40}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{5}{ 40}$

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

$\dashrightarrow\sf v = 8 \: cm$

thus, the image distance is 8 cm.

» The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and is also equal to the ratio of height of the image to the height of the object .i.e.,

$\boxed{ \bf m = - \dfrac{v}{u} = \dfrac{h'}{h}}$

where,

• v denotes image distance
• u denotes object distance
• h' denotes image height
• h denotes object height

By substituting all the given values in the formula,

$\dashrightarrow\sf - \dfrac{v}{u} = \dfrac{h'}{h}$

$\dashrightarrow\sf - \dfrac{8}{ - 40} = \dfrac{h'}{8}$

$\dashrightarrow\sf \dfrac{1}{5} = \dfrac{h'}{8}$

$\dashrightarrow\sf h' = \dfrac{8}{5}$

$\dashrightarrow\sf h' = 1.6 \: cm$

Thus, the image height is 1.6 cm