At age 45, a person is fitted for reading glasses that have a power equal to 2.2

Question

At age 45, a person is fitted for reading glasses that have a power equal to 2.23 D in order to read at 25.0 cm. By the time she reaches the age of 55, she discovers herself holding her newspaper at a distance of 42.0 cm in order to see it clearly with her glasses on. Assume the glasses are placed 2.2 cm from her eyes.

a) Where was her near point at age 45?

(b) Where is her near point at age 55?

(c) What power is now required for the lenses of her reading glasses so that she can again read at 25.0 cm?

Explanation / Answer

a)power of normal eye for reading at 25cm

1/f=1/u +1/v

=1/0.25+ 1/0.022 =49.45

But she needs a lens of 2.23 D, it means her power is 49.45-2.23=47.22D

47.22=1/u + 1/0.022

1/u =1.77

u= 0.565m =56.5cm

(b)P' = 1/0.45 + 1/0.022 =45.45+2.22=47.67

After removing the glasses, her power = 45.44

lets near point be u

45.44=1/u+1/0.022

hence u tends to infinity. Her near point at 55 will be infinity.

c) She needs a power of 49.45-45.44= 4.01 D

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