Answer to Question #153490 in Optics for Stephanie Anthony

Question

A converging lens of focal length 20.0 cm forms an image of each of two objects placed (a) 40.0 cm and 

(b) 15.00 cm in front of the lens. In each case, find the image distance and describe the image

Answer 1

$(a) \; f = -20 \;cm \\ p = 40 \;cm \\ \frac{1}{q}=\frac{1}{f}-\frac{1}{p} \\ = -\frac{1}{20}- \frac{1}{40} \\ \frac{1}{q}=\frac{-60}{800} \\ q = -13.3 \;cm \\ M = \frac{-q}{p} \\ = \frac{13.3}{40}=0.33$

Hence the image is smaller than the object.

$(b) \; f = -20 \;cm \\ p = 15 \;cm \\ \frac{1}{q}=-\frac{1}{20}- \frac{1}{15} \\ \frac{1}{q} = -\frac{35}{300} \\ q = -8.5 \;cm \\ M = 0.56$

Hence the image is smaller than the object.