Question

A slide projector needs to create a 98.0 cm -high image of a 2.20 cm -tall slide. The screen is 308 cm from the slide.

1. What focal length does the lens need? Assume that it is a thin lens.

2. How far should you place the lens from the slide?

Answer 1

Projector needs to create a 98.0 cm -high image h'= 98.0 cm

Object 2.20 cm -tall slide. h= 2.20 cm

The screen is 308 cm from the slide. u+v = 308 cm

Magnification (m) = h/h’

m = 98.0/2.20

= 44.5454545

m = h’/h = -v/u

u+v = 308 cm ,-v/u = 44.5454545

u= 7.073cm v= 300.927cm

Thin Lens Equation

1/f= 1/u + 1/v

On substituting above values

f = 6.91cm

1.Focal length of the lens = 6.91cm

2.Lens should be placed 300.927cm far from the screen and 7.073cm far from slide.