A slide projector is required to project a 35 mm slide ( 35 mm 23 mm ) onto a 2 m 2 m screen located at a distance of 10 m from the lens. Determine the focal length of the projector's lens.

Step-by-step solution

To project the entire slide onto the screen, the maximum magnification is determined by fitting the larger dimension of the slide ( 35 mm ) onto the screen ( 2 m ). Magnification m = v |u| = 2000 mm 35 mm = 400 7 Given the image distance v = 10 m = 1000 cm , the object distance |u| is: |u| = v m = 1000 400 7 = 17.5 cm Using the sign convention, u = -17.5 cm and v = +1000 cm . Applying the lens formula: 1 f = 1 v - 1 u 1 f = 1 1000 - (- 1 17.5 ) 1 f = 1 1000 + 1 17.5 = 17.5 + 1000 17500 = 1017.5 17500 f = 17500 1017