A lost camper starts a fire by using a lens from his eyeglasses to focus sunligh

Question

A lost camper starts a fire by using a lens from his eyeglasses to focus sunlight on kindling 5.5 cm from the lens. The camper has a near point of 17.0 cm. When the lens is used as a simple magnifier, give values for the following conditions. a) What is the maximum magnification that can be achieved assuming a normal eye? b) What is the actual maximum magnification that can be achieved for this camper? c) What is the magnification assuming the eye is normal and relaxed? d) What is the actual magnification assuming the camper's eye is relaxed?

Explanation / Answer

a )   focal length of the lens = f = 5.5 cm

for a normal eye , the near point is at 25 cm

so di =image distance= - 25 cm

using lens equation :

1/f = 1/di + 1/do

1/5.5 = 1/-25 + 1/do

so do = 4.51 cm

So maximum magnification = -di/do = -(-25)/4.51 = 5.54

b) focal length of the lens = f = 5.5 cm

near point of camper = 17 cm

so di = - 17 cm

using lens equation :

1/f = 1/di + 1/do

1/5.5 = 1/-17 + 1/do

so do = 4.16 cm

So magnification = -di/do = -(-17)/4.16 = 4.08

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