Foundation
Physics Foundation
Human Eye And Colorful World
Question

A certain child’s near point is 10.0 cm ; her far point(with eyes relaxed) is 125 cm. Each eye lens is 2.00 cm from the retina. (a) Between what limits, measured in diopters, does the power of this lens–cornea combination vary? (b) Calculate the power of the eyeglass lens the child should use for relaxed distance vision. Is the lens converging or diverging?

JEE Advance
College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Solution
Verified BY
Verified by Zigyan

(a) when child clearly sees objects at her far point the lens cornea combination has assumed a focal length suitable for forming the image on the retina. Using the lens equation ,
1f=1v-1u, Also power P=1f

Here, u = –125 cm = –1.25m and v = 2 cm = 0.02 m
Pfar=1f=11.25+10.02=+50.8 Diopters
Similarly, when eye is focused on object at near point, the optical power of lens cornea combination is 
Pnear=1f=10.1+10.020=+60 Diopters
Hence, the range of the power of lens cornea combination is + 50.8 Diopters ≤ P ≤ 60.0 Diopters 
(b) if child sees very distant object clearly, her eyeglass lens must form an erect, virtual image for the object at infinity at the far point of her eye, optical power of required lens is,
P=1u+1v=0+1-0.125=-0.8000 Diopters
Since the power and hence the focal length of this lens is -ve, it is diverging.
Lock Image

Please subscribe our Youtube channel to unlock this solution.