Question

An object is placed at 10 cm in front of a convex lens of radius of curvature 40 cm then find the position and nature of the image ?​

Answer 1

Given :

In convex lens,

Object distance = - 10cm

Radius of curvature = 40 cm

To find :

The position and the nature of the image.

Solution :

we know that the focal length of the spherical mirror is equal to half of its radius of curvature

f = R/2

f = 40/2 = 20 cm.

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,

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

$\leadsto{ \bf \dfrac{1}{v} - \dfrac{1}{( - 10)}= \dfrac{1}{20}}$

$\leadsto{ \bf \dfrac{1}{v} + \dfrac{1}{10}= \dfrac{1}{20}}$

$\leadsto{ \bf \dfrac{1}{v} = \dfrac{1}{20} - \dfrac{1}{10}}$

$\leadsto{ \bf \dfrac{1}{v} = \dfrac{1 - 2}{20} }$

$\leadsto{ \bf \dfrac{1}{v} = \dfrac{ - 1}{20} }$

$\leadsto{ \bf v = - 20 \: cm}$

Thus, the position of image is -20 cm.

Nature of image :

• The image is erect and virtual.