Question

A mother sees that her child’s glasses prescription is 2.5 D. When being worn, the glasses are 2.20 cm from the child's eyes. What is the child's near point, in centimeters? Assume the near point for normal human vision is 25.0 cm.

Answer 1

f = 1/P

f = 1/ 2.5

f = 0.4 m

normal near point = 25 cm

distance to glasses = 2.2 cm

so,

object distance = 22.8 cm = 0.228 m

if x is the near point then

image distance = x - 0.022

this should be negative as image is in front of the lens

so,

using lens equation

1/f = 1/object distance + 1/image distance

1/0.4 = 1/ 0.228 - 1/ x - 0.022

-1.885 = - 1/ x - 0.022

x - 0.022 = 0.53023

x = 0.55223 m

or

x = 55.223 cm