Question

A point object is placed at a distance of 18 cm from a convex lens on

its principal axis. Its image is formed on the other side of the lens at

27 cm. Calculate the focal length of the lens.​

Answer 1

Answer:

the focal length is 7.5cm

Answer 2

Given :

In convex lens,

Object distance : - 18 cm

Image distance : 27 cm

To find :

The focal length of the lens

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,

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

$\dashrightarrow \sf \dfrac{1}{27} - \dfrac{1}{-18}= \dfrac{1}{f}$

$\dashrightarrow \sf \dfrac{1}{27} + \dfrac{1}{18}= \dfrac{1}{f}$

$\dashrightarrow \sf \dfrac{2 + 3}{54}= \dfrac{1}{f}$

$\dashrightarrow \sf \dfrac{5}{54}= \dfrac{1}{f}$

$\dashrightarrow \sf f = \dfrac{54}{5}$

$\dashrightarrow \sf f = 10.5 cm$

Thus, the focal length of the lens is 10.5 cm