An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio `3: 2`. What is the distance between the screen and the object?

Options

A. 124.5 cm
B. 144.5 cm
C. 65.0 cm
D. 99.0 cm

Answer

D

Explanation

Given : Separation of lens for two of its position, `d=10cm`
Ratio of size of the image in two positions `(I_(1))/(I_(2))=(3)/(2)`
Distance of object from the screen, `D=?`
Applying formula,
`(I_(1))/(I_(2))=((D+d)^(2))/((D-d)^(2))rArr (3)/(2) =((D+10)^(2))/((D-10)^(2))`
On solving, we get D = 99 cm
Hence the distance between the screen and the object is 99 cm.