Question

You wish to project the image of a slide on a screen 9.50 m from the lens of a slide projector.

1) if the slide is palced 13 cm from the lens what focal length lens is required

2) if the dimensions of the picture on a 35-mm color slide are 24mmx36mm what is the minimum size of the projector screen required to accommodate the image?

Answer 1

Given data

(1)

Distance of slide from the lens (object distance) u = 13 cm = 130 mm

Distance of between lens and screen (image distance), v = 9.5 m = 9500 mm

then focal length of the lens can be obtained as follows

1/f = 1/u + 1/V

1/f = (1/130)+(1/9500)

f = (9500*130)/(9500+130)

f = 128.25 mm

(2)

Distance of slide from the lens (object distance), u = 13 cm = 130 mm

Distance of between lens and screen (image distance), v = 9.5 m = 9500 mm

It is given that, length and height of slide is l * h = 24 mm * 36 mm

Magnification of the given lens is

M = -v / u

M = - 9500/130

M = -73.077

Negative indicates that the image will be inverted. and magnified by a factor 73.077

Therefore the minimum size of the screen can be obtained as follows

l = 24 * 73.077 = 1753.85 mm = 1.754 m

h = 36 * 73.077 = 2630.77 mm = 2.631 m