3. You and a colleague are out looking for rare plants. Your colleague is nearsi

Question

3. You and a colleague are out looking for rare plants. Your colleague is nearsighted, but she wears eyeglasses to correct it. Her correction is -3.75 Diopters for each lens. You have normal vision-no correction needed. You're trying to use a magnifying glass (with your eye right next to that lens, as it is designed for) to view a small plant growing in rock crevice. But due to the narrowness of the crevice you can't get the large magnifying lens ( 10.0 cm) close enough to the plant to use it as intended-with normal comfortable viewing (ie, with the object " at" the focal point). Your colleague has just completed PH 212, so she knows just what to do: She removes one lens from her eye- glasses and is able to place it so that your magnifier can then offer normal comfortable viewing for you. If the two lenses are then 2.50 cm apart, what is the distance from the magnifying glass to the plant? g.

Explanation / Answer

3. g. power of each lens. P = -3.75 D

now, focal length, f = 1/P = -0.26 m = -26.666 m

distance betwen two lenses, d = 2.5 cm

focal length of the magnifying glass, fo = 10 cm

hence normal final image distance = v

1/v - 1/u = 1/fo

u = fo

hence

v = fo = 10 cm from the magnifying glass

distnac eof magnifying glass to the plant = u

then

for magnifying glass

1/v' - 1/u = 1/fo

for eyelens

1/v - 1/u' = 1/f

but u' = v' - d

hence

1/v' - 1/u = 1/10

1/10 - 1/u' = 1/(-26.666)

hence

u' = 7.2727 cm

v' = 9.772 cm

hence

u = 430 cm

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