Question

C Exercise 25.18 5 of 10 Review 1 Constants l Periodic Table Part A Bifocal glasses are used to correct both nearsightedness and farsightedness at the same time. (Figure 1) If the near points in the right and left eyes are 34.0 cm and 48.0 cm, respectively, and the far point is 230 cm for both eyes, what are the powers of the lens prescribed for the right eye? (Assume that the glasses are worn 3.00 cm from the eyes.) Enter your answers in ascending order separated by commas. P,=-0.441, 1.22 Submit Incorrect; Try Again; 2 attempts remaining Figure Part B of 1 What are the powers of the lens prescribed for the left eye? Enter your answers in ascending order separated by commas. P-.0.441,2.22 corectioN Previous Answers Request Answer Submit Incorrect; Try Again; 4 attempts remaining

Answer 1

PART A:

For the right eye

The near point is at 34 cm ( 0.34 m ).

To correct this the lens must produce the image at 0.34 m from the eyes if an object is placed at 0.25 m from the eyes.

As the distance between the lens and the eye is 3 cm ( 0.03 m), the object distance and the image distances are as follows

d,-ー0.34 ±0.03ーー0.31 m

d0.25-0.030.22 m

So, the power of the lens for farsightedness is

1.32 D do d 0.22-0.31

Now, the far point is 230 cm ( 2.3 m )

To correct this the lens must produce the image at 2.3 m from the eyes if an object is placed at infinity.

As the distance between the lens and the eye is 3 cm ( 0.03 m), the object distance and the image distances are as follows

d,ー_2.30+ 0.03一一2.27 m

$d_o=\infty$

So, the power of the lens for nearsightedness is

do d 一2.27 =-0.44 D

PART B:

For the left eye

The object distance and the image distances for this case are as follows

d,ーー0.48 ±0.03 -0.45 m

d0.25-0.030.22 m

So, the power of the lens for farsightedness is

0.22 +-0.45 = 2.32 D d. di

And for nearsightedness, the power is the same as in right eye. i.e

do d 一2.27 =-0.44 D

So, the final answer is ( you might need to put a space after the comma )

Р,.-- 0.44,1.32

Pー-0.44, 2.32