Question

Find the focal length of contact lenses that would allow a nearsighted person with a 130 cmcm far point to focus on the stars at night.

Answer 1

130cm

Step-by-step explanation:

The lens equation is expressed as;

1/f = 1/u+1/v where;

f is the focal length of the lens

u is the object distance

v is the image distance

Since the near sighted person wants focus the starts at nigt, the stars at night are the images located that infinity. Hence the image distance v = ∞.

The object distance u = 130cm

Substituting the given parameters in the formula to get the focal length f

`(1)/(f) = (1)/(\infty) + (1)/(130) \\\\As \ x \ tends \ to \ \infty, \, (a)/(x) \ tends \ to \ 0 \ where\ 'a' \ is \ a\ constant \\\\} \\\\`

`(1)/(f) = 0+ (1)/(130)\\\\`

`(1)/(f) =(1)/(130)\\cross\ multiply\\\\f = 130*1\\\\f = 130cm`

Hence the focal length of contact lenses that would allow a nearsighted person with a 130 cm far point to focus on the stars at night is 130cm