The cornea of the eye has a radius of curvature of approximately 0.42 cm , and t

Question

The cornea of the eye has a radius of curvature of approximately 0.42 cm , and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is around 25.0 mm .

What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea?

A- Express your answer using two significant figures. unit (mm)

Explanation / Answer

form the lens maker's formula

(n1/do)+(n2/di) = (n2-n1)/R

do is the object distance = infinite

di = image distance = 25 mm = 2.5 cm

n1 is the refractive index of air = 1

(1/infinite)+(1.35/2.5) = (1.35-1)/R

0+(1.35/2.5) = 0.35/R

1.35/2.5 = 0.35*R

1.35*R = 2.5*0.35

R = 2.5*0.35/1.35 = 0.648 cm = 6.48 mm

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