The cornea of the eye has a radius of curvature of approximately 0.58 cm , and t

Question

The cornea of the eye has a radius of curvature of approximately 0.58 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?

Express your answer in mm using two significant figures.

Explanation / Answer

To focus on the retina, the focal length has to be 25 mm

Now, the approximate formula for focal length of a thin lens is

f = R n2 / (n2 - n1 )

where n2 is here 1.35

n1 = 1 (of air)

and as sais before, f needs to be 25 cm

So, 25 = R x 1.35 / (1.35 - 1 )

R = 25 x 0.35 / 1.35 = 6.48148 mm

So, radius of curvature needs to be R = 6.48 mm or 0.648 cm.

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