A transparent photographic slide is placed in front of a converging lens with a

Question

A transparent photographic slide is placed in front of a converging lens with a focal length of 2.29 cm. An image of the slide is formed 11.2 cm from the slide. (a) How far is the lens from the slide if the image is real? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) cm cm (b) How far is the lens from the slide if the image is virtual? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) cm cm

Explanation / Answer

from the lens equation

1/f =1/p + 1/q

since p+q =11.2 cm

q = 11.2-p

1/2.29 = 1/p + 1/11.2-p

p^2 -(11.2) p + 25.64 cm^2 = 0

solving quadratic equation

p = 7.99 cm or 3.2 cm

(b)

if the image is virtual

q = -11.2- p

1/2.29 = 1/p - 1/(11.2+p)

p^2 + 11.2p - 25.64 cm^2

solving quadratic eqation

p = 1.94 cm or p = -13.14 cm

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