Question

A slide projector has to project a 35 mm slide (35 mm × 23 mm) on a 2 m × 2 m screen at a distance of 10 m from the lens. What should be the focal length of the lens in the projector?

Answer 1

The focal length of the lens in the projector is f = 17.19 cm .

Explanation:

Given data in the question  :

Object height or size is 35 mm = 3.5  cm

And image size = 2 m

And image distance is 10 m from the lens

The magnification needed for the projector is provided ,

$M=\frac{v}{u}=\frac{200}{3.5}$

$\frac{1000}{u}=\frac{200}{3.5}$

$\frac{3500}{u}=200$

200 u = 3500

$u=\frac{3500}{200}$

u = 17.5 cm

[ 35 mm > 23 mm, so the magnification takes target dimension 35 mm ]

Now we know that,  

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{-u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{1000}+\frac{1}{17.5}=\frac{1}{f}$

$0.001+0.057=\frac{1}{f}$

$0.0581=\frac{1}{f}$

Reciprocal both side , we get

f = 17.19 cm .

Thus, the focal length f = 17.19 cm .