Question

find focal length and hence power of a convex lens which produces a real image at a distance of 60cm from a lens. When an object is placed at a distance of 40cm in front of the lens.
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Answer 1

Given :

In convex lens,

Image distance = 60cm

Object distance = - 40cm

To Find :

The focal length and power of the convex 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,

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

$\dashrightarrow{ \sf \dfrac{1}{60} - \dfrac{1}{( - 40)}= \dfrac{1}{f}}$

$\dashrightarrow{ \sf \dfrac{1}{60} + \dfrac{1}{( 40)}= \dfrac{1}{f}}$

$\dashrightarrow{ \sf \dfrac{2 + 3}{120}= \dfrac{1}{f}}$

$\dashrightarrow{ \sf \dfrac{1}{f}= \dfrac{5}{120}}$

$\dashrightarrow{ \sf \dfrac{1}{f}= \dfrac{1}{24}}$

$\dashrightarrow{ \sf f = 24 \: cm}$

We know power is the reciprocal of focal length that is,

$\sf P = \dfrac{1}{f}$

$\sf P = \dfrac{100}{24}$

$\sf P = 4.1 \: D$

The focal length of the lens is 24cm and power is 4.1 D.