Question

The crystalline lens of the human eye is double convex and has a typical range of optical power from 110 diopters to 150 diopters .

Part A

What is the range of focal lengths the eye can achieve?

Enter your answers in millimeters, separated by a comma, to three significant figures.

Part B

At minimum power, where does it focus the image of a very distant object?

Give your answer as the distance, in millimeters, from the crystalline lens of the eye to the image to three significant figures.

Part C

At maximum power, where does it focus the image of an object at the near point of 25.0 cm ?

Give your answer as the distance, in millimeters, from the crystalline lens of the eye to the image to three significant figures.

Answer 1

power of the lens P = 1/f

focal length is f = 1/P = 1/110 = 0.00909 m = 0.00909*1000 = 9.09 mm

P = 150 diopters

f = 1/150 = 0.00666 m = 6.66 mm

PART A

So the range of focla lengths are 9.09 mm to 6.66 mm

PART B

At minimum Power

focal length is f = 9.09 mm

object distance is do = infinite

then

1/f = (1/do)+(1/di)

1/9.09 = (1/infinite)+(1/di)

di = 9.09 mm

PART C

at maximum Power

f = 6.66 mm

do = 25 cm = 250 mm

then

1/f = 1/do + 1/di

(1/6.6602) = (1/250)+(1/di)

di = 6.67 mm