You are designing a projection system for a hall having a screen measuring 4.05m

Question

You are designing a projection system for a hall having a screen measuring 4.05m square. The lens of a 35.0mm slide projector in the projection booth is 15.2m from this screen. You want to focus the image of 35.0mm slides (which are x = 24.0mm, y = 36.0mm onto this screen so that you can fill as much of the screen as possible without any part of the image extending beyond the screen.

Part A) What focal-length lens should you use in the projector?

Part B) How far from the lens should the slide be placed?

Part C) What are the dimensions of the slide's image on the screen?

Explanation / Answer

Start with h'/h = q/p

4050/36 = 15200/p

p = 135 mm

So the lens is 135 mm from the slide (13.5 cm)

1/f = 1/p + 1/q

1/f = 1/135 + 1/15200

f = 133.8 mm (13.38 cm)

The dimensions of the slide image will be...

h'/24 = 15200/135

h' = 2.702 m by 4.05 m

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