A slide projector produces 500 times enlarged image of a slide on a screen 10 m away. Assume that the projector consists of a single convex lens used for magnification. If the screen is moved 2.0 m closer, by what distance should the slide be moved towards or away from the lens so that the image remains focused on the screen ? What is the magnification in this case ?

Explanation

In the first casse, `upsilon = 10 m and (upsilon)/(u) = -500.`
Thus, `u = -(upsilon)/(500) = (1)/(50)m = - 2.0 cm.` The focal length f is given by
`(1)/(f) = (1)/(upsilon) - (1)/(u) = (1)/(10m) + (1)/(2.0cm).`
If the screen is moved 2.0 m closer, `upsilon = 8.0m.` The object distance u' is given by
`(1)/(upsilon) - (1)/(u') = (1)/(f)`
or, `(1)/(u) = (1)/(upsilon) - (1)/(f) = (1)/(8.0m) - (1)/(10m) - (1)/(2.0 cm)`
`=(1)/(40m) - (1)/(2.0cm)`
`=-(1)/(2.0cm) - ((1) - (1)/(2000))`
or, `u' = -2.0 cm (1 - (1)/(2000))^(-1)`
`~~ - 2.0 cm (1 + (1)/(2000)) = - 2.0cm - (1)/(1000)cm.`
Thus, the slide should be taken `(1)/(1000)cm` away from the lens.