Question

A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +1.75 diopters. With these eyeglasses, what is the near point of the machinist?

Answer 1

17.4 cm

Step-by-step explanation:

Power of lens = +1.75 diopters

Focal length of lens

`f=(100)/(1.75)=(400)/(7)`

This is a convex lens as focal the diopter given is positive which makes the focal length positive. Image distance will be negative.

v = -25

`(1)/(v)-(1)/(u)=(1)/(f)\\\Rightarrow (1)/(-25)-(1)/(u)=(1)/((400)/(7))\\\Rightarrow -(1)/(u)=(7)/(400)+(1)/(25)\\\Rightarrow (1)/(u)=-(7)/(400)-(1)/(25)\\\Rightarrow (1)/(u)=-0.0575\\\Rightarrow u=-17.4\ cm`

∴ The new near point is 17.4 cm