Question

7. A farsighted man uses eyeglasses with a refractive power of 2.00 diopters. Wearing the glasses 0.020 m from his eyes, he is able to read books held no closer than 0.304 m from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?
diopters

Answer 1

i solved this question before just change the value and definetely you will got the answer

A farsighted man uses eyeglasses with a refractive power of 2.25 diopters. Wearing the glasses 0.03 m from his eyes, he is able to read books held no closer than 0.26 m from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters? ____________ diopters

The focal length, "fd" of the lens of diopter +2.25 for the farsighted man = -(1/2.25) = -4/9 m
The corrected focal length, F of the eye if uncorrected is f are related by
1/F = 1/f + 1/fd -0.03/(f*fd)----------------------------... 1
If fc is the focal length of contact lens, we have
1/F = 1/f + 1/fc ----------------------------------------... 2
Equating RHS of 1 and 2 we get
1/fc = 1/fd -0.03/(f*fd)----------------------------... 3
Substituting F= 0.26 and fd = -4/9 in 1 we get
1/0.26 = 1/f - 9/4+ 0.27/(4f), multiplying by 4*f*0.26, we have
4*f = 1.04 - 2.34*f + 0.07 or
6.34*f = 1.11 or f = 1.11/6.34 = 0.175 or from 3
1/fc = -9/4+{0.27/(4*0.175)} = -2.25 + 0.385 = -1.864 or fc = -0.536 m or 53.6 cm diverging lens of +1.86 diopter