Question

A certain slide projector has a 100 mm focal length lens. (a) How far away is the screen, if a slide is placed 103 mm from the lens and produces a sharp image? (b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the image? Explicitly show how you follow the steps in the Problem-Solving Strategy for lenses.

Answer 1

Focal Length of lens, f= 100mm

Distance of slide from lens, u= 103mm

Let distance of screen from lens be "v", then using Lens Equation,

1/f= 1/v+ 1/u

1/v= 1/f - 1/u

v = uf/u - f

using given values in above,

   [v= (100)(103)/{103-100}= 3433.334mm= 3.43 m (ANS)

b). In this we'll use the formula of magnification in which if "I" is the size of image and "O" is the size of object then

   [\frac{I}{O}= \frac{-v}{u}]

using given and calculated values in above,

   [\frac{I}{24.0 by 36.0mm}= \frac{-3433.33}{103}]

   [I= 799.99by 1199.99mm= 0.799 by 1.199 m]