Solveeit Logo
Login

Question

Question: A screen is placed 90 cm away from an object. The image of the object on the screen is formed by a c...

A screen is placed 90 cm away from an object. The image of the object on the screen is formed by a convex lens at two different location separated by 20 cm. Find the focal length of lens.:

A

42.8 cm

B

21.4 cm

C

10.7 cm

D

5.5 cm

Answer

21.4 cm

Explanation

Solution

: The image of the object can be located on the screen for two positions of convex lens such that u and v are exchanged.

The separation between two positions of the lens is d = 20 cm

From the figure,

v1−u1=20 cm\mathrm { v } _ { 1 } - \mathrm { u } _ { 1 } = 20 \mathrm {~cm}

Solving

v1=55 cm,u1=35 cm\mathrm { v } _ { 1 } = 55 \mathrm {~cm} , \mathrm { u } _ { 1 } = 35 \mathrm {~cm}

From lens formula,

or

⇒f55×3590=2.14 cm\Rightarrow \mathrm { f } \frac { 55 \times 35 } { 90 } = 2.14 \mathrm {~cm}