The projection lens in a certain slide projector is a single
thin lens. A slide 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The slide-to-screen
distance is 3.00 m. (a) Determine the focal
length of the projection lens. (b) How far from the
slide should the lens of the projector be placed to form the image on the screen?

Question

The projection lens in a certain slide projector is a single
thin lens. A slide 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The slide-to-screen
distance is 3.00 m. (a) Determine the focal
length of the projection lens. (b) How far from the
slide should the lens of the projector be placed to form the image on the screen?

parthkohli · Answer

A magnified image. Sounds like a convex lens.

parthkohli · Answer

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parthkohli · Answer

$$\dfrac{v}{u} = \dfrac{h_i}{h_o}=\dfrac{1800}{24} = 75 $$

parthkohli · Answer

$v = 75 u$ and $u + v = 3$.

So $u = \frac{3}{76}$ and $v = \frac{225}{76}$.

parthkohli · Answer

The focal length is now easily calculable.

parthkohli · Answer

$$\dfrac{225}{3}+\dfrac{76}{3} = \dfrac{1}{f}$$$$f = \dfrac{3}{301}m = 1 cm$$