Question

A mother sees that her child's glasses prescription is 0.75 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

Solution :

Given :

Power of lens (P) = 0.75 D

Since : f = 1/P = 1 / (0.75 D) = 1.33 m

And, we have :

Near point for Normal vision = 25 cm

Distance of glasses from the eyes = 2.2 cm

Thus : Object distance (u) = 25 cm - 2.2 cm = 22.8 cm = 0.228 m

Let, the near point for the eye be : x

Therefore: Image distance (v) = x - 0.022 m

Now Using lens equation :

1/f = 1/u + 1/v

1/1.33 = 1/ 0.228 - 1/ (x - 0.022)

1/1.33 = 1/ 0.228 - 1/ (x - 0.022)

-3.636 = - 1/ (x - 0.022)

x - 0.022 = 0.275

x = 0.297 m = 29.7 cm