Question

An object of height 8 cm is placed at a distance of 40 cm in front of a convex lens of focal length 20 cm the size of image is​

Answer 1

Given :

In convex lens,

Object height = 8 cm

Object distance = - 40cm

focal length = 20 cm

To find :

The size of image

Solution :

Firstly we have to find image distance.

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 :

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

here,

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

by substituting all the given values in the formula,

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

$\leadsto{ \sf \dfrac{1}{v} - \dfrac{1}{ - 40}= \dfrac{1}{20}}$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{1}{20} - \dfrac{1}{40}}$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{2 - 1}{40} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{1}{40}}$

$\leadsto{ \sf v = 40 \: cm}$

thus, the image distance is 40cm.

Now, using magnification formula i.e.,

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

here,

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

by substituting all the given values,

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

$\leadsto{ \sf \dfrac{h'}{8} = \dfrac{40}{40}}$

$\leadsto{ \sf {h'} = 8 \: cm}$

thus, the size of the image is 8 cm.