A small lightbulb is 1.02 m from a screen. Part A If you have a convex lens with

Question

A small lightbulb is 1.02 m from a screen. Part A If you have a convex lens with 20 cm focal length, where are the two lens locations that will project an image of the lightbulb onto the screen? Express your answers using two significant figures separated by a comma. Hints between the lightbulb and the screen at d1, d2 = cm from the lightbulb Part B What’s the magnification in the first case (smaller distance from the lightbulb)? Part C What’s the magnification in the second case (larger distance from the lightbulb)?

Explanation / Answer

f = 0.20 m

Suppose object is at distance p from lens,

then image distance from lens, q = 1.02 - p

Applying lens equation,

1/f = 1/p + 1/q

1/0.20 = 1/p + 1/(1.02 - p)

5 = (1.02 - p + p ) / (p (1.02 - p))

5 = 1.02 / (1.02p - p^2)

5.1p - 5p^2 = 1.02

5 p^2 - 5.1p + 1.02 = 0

p = 0.747 and 0.273 m

d1, d2 =27.3 cm, 74.7 cm

(b) m = - q / p = - 74.7 / 27.3

m = - 2.74

(c) m = - 27.3 / 74.7

m = - 0.365

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