The projection lens in a certain slide projector is a single thin lens. A slide

Question

The projection lens in a certain slide projector is a single thin lens. A slide 23.8 mm high is to be projected so that its image fills a screen 1.74 m high. The slide-to-screen distance is 3.08 m. (Enter your answers to at least one decimal place.) Determine the focal length of the projection lens. You appear to be using 3.08 m incorrectly as the image distance. mm How far from the slide should the lens of the projector be placed to form the image on the screen? If the object is located at the focal point the image is formed at infinity. mm

Explanation / Answer

u+v = 3.08m
magnification m = v / u = 1.74 / 0.0238 = 73.1
so v = 73.1*u
so u + 73.1*u = 3.04m
u = 3.08 / 74.1 = 0.04156 m
so v = 73.1*u = 73.1* 0.04156 m = 3.038 m

(a) focal length f = u*v / (u+v) = 0.04156 * 3.038 / 3.0800 = 0.04113 = 40.999 mm
(b) from above, distance from slide to lens is u = 0.04156 m = 41.56 mm

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