Sometimes a person cannot clearly see objects close up or far away. To correct t

Question

Sometimes a person cannot clearly see objects close up or far away. To correct this type of vision, bifocals are often used. The top half of the lens is used to view distant objects ana the bottom half of the lens is used to view objects close to the eye. A person can clearly see objects only if they are located between 34 cm and 164 cm away from her eyes. Bifocal lenses are used to correct her vision. What focal length lens (in cm) should be used in the bottom half of the lens to allow her to clearly see objects 25 cm away? What focal length lens (in cm) should be used in the top half of the lens to allow her to clearly see distant objects?

Explanation / Answer

here ,

for the bottom half of the lens

for the focal length of the lower bottom

image distance , di = - 34 cm

object distance , do = 25 cm

1/f = 1/di + 1/do

1/f = -1/34 + 1/25

solving for f

f = 94.4 cm

the focal length of bottom half is 94.4 cm

b)

for the top half

di = -164 cm

1/f = 1/infinite

1/f = -1/164

f = - 164 cm

the focal length pof the upper half of lens is -164 cm

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