Question

Find the image distance and size of the image if object of height 10 cm is placed at distance of 50 cm in front of concave lens with focal length 20 cm.​

Answer 1

Given :

In concave lens,

Object height = 10cm

Object distance = - 50cm

Focal length = -20cm

Note : In concave lens focal length and image distance is denoted by negative sign.

To find :

Theimage distance and the size of the image.

Solution :

using lens formula that is,

» The formula which gives the relationship between image distance, object distance and focal length of a lens is known as the lens formula.

The lens formula can be written as :

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

where,

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

by substituting all the given values in the formula,

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

$\dashrightarrow \sf \dfrac{1}{v} - \dfrac{1}{( - 50)}= \dfrac{1}{( - 20)}$

$\dashrightarrow \sf \dfrac{1}{v} + \dfrac{1}{50}= - \dfrac{1}{ 20}$

$\dashrightarrow \sf \dfrac{1}{v} = - \dfrac{1}{ 20} - \dfrac{1}{50}$

$\dashrightarrow \sf \dfrac{1}{v} = \dfrac{ - 5 - 2}{100}$

$\dashrightarrow \sf \dfrac{1}{v} = \dfrac{ - 7}{100}$

$\dashrightarrow \sf v = - \dfrac{100}{7}$

$\dashrightarrow \sf v = - 14.2 \: cm$

Thus, the image distance is -14.2 cm.

We know that,

» The ratio of image distance to the object distance is equal to the the ratio of image height to the image height

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

$\dashrightarrow \sf \dfrac{h'}{10} = \dfrac{ - \dfrac{100}{7} }{ - 50}$

$\dashrightarrow \sf \dfrac{h'}{10} = \dfrac{100}{7 \times 50}$

$\dashrightarrow \sf \dfrac{h'}{10} = \dfrac{2}{7 }$

$\dashrightarrow \sf h'= 2.85 \: cm$

Thus, the size of the image is 2.85 cm