Question

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 distance of the film from the projection lens and focal length of projection lens.

• A. 7 cm, 70 mm
• B. 6 cm, 60 mm
• C. 5 cm, 50 mm
• D. 4 cm, 40 mm

Answer 1

The correct option is A 7 cm, 70 mm

As in the case of projector,$m=\frac{I}{O}=\frac{v}{u}$
So, $-\frac{20\times 100cm}{3.5cm}=\frac{40\times 100}{u}$
$⟹u=-7cm$i.e., the film is at a distance of $7cm$ in front of the projection lens.
And from the lens formula we have,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$⟹\frac{1}{f}=\frac{1}{4000}-\frac{1}{-7}$
$⟹f=7cm=70mm$ [as $\frac{1}{4000}<<\frac{1}{7}$]
i.e., focal length of projection lens is $70mm$.