JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Curved Surfaces

A 35 mm film is to be projected on a 20 m wide screen situated at a distance of 40 m from the film-projector. Calculate the focal length of projection lens.

A) 70 mm

B) 35 mm

C) 40 mm

D) 20 mm

Correct Answer: A

Solution :

[a]

As in case of projector, \[m=\frac{I}{O}=\frac{v}{u}\]

So, \[-\frac{20\times 100\,cm}{3.5\,cm}=\frac{40\times 100}{u}\]

i.e., \[u=-7\text{ }cm\]

i.e., film is at a distance of 7 cm in front of projection lens.

And from lens formula \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f},\] here we have \[\frac{1}{4000}-\frac{1}{-7}=\frac{1}{f}\] or \[\cong 7\,cm=70\,mm\]

[as (1/4000) << (1/7)]

i.e., focal length of projection lens is 70 nun.