Question

A convex lens produces a real image of an object thrice of its size. If the focal length is 25 cm. Calculate object and image distance of the object​

Answer 1

Given :

In convex lens,

Image distance = 3 × object distance

Focal length = 25 cm

To Find :

The object distance and image distance.

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,

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

$\dashrightarrow{ \sf \dfrac{1}{3u} - \dfrac{1}{u}= \dfrac{1}{25}}$

$\dashrightarrow{ \sf \dfrac{1 - 3}{3u} = \dfrac{1}{25}}$

$\dashrightarrow{ \sf \dfrac{ - 2}{3u} = \dfrac{1}{25}}$

$\dashrightarrow{ \sf 3u = - 2 \times 25 }$

$\dashrightarrow{ \sf 3u = - 50 }$

$\dashrightarrow{ \sf u = \dfrac{ - 50}{3} }$

$\dashrightarrow{ \sf u = 16.6 \: cm}$

Thus, the object distance of the lens is 16.6 cm.

we know that,

Image distance = 3 × object distance

= 3 × 16.6 = 50 cm.

Thus, the image distance is 50 cm.