A Nearsighted Eye. A certain very nearsighted person cannot focus on anything fa

Question

A Nearsighted Eye. A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye. In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina. If the radius of curvature of the cornea is 0.65 cm when the eye is focusing on an object 36.0 cm from the cornea vertex and the indexes of refraction are as described before, what is the distance from the cornea vertex to the retina? Express your answer to two significant figures and include the appropriate units. What does this tell you about the shape of the nearsighted eye? This distance is shorter than for the normal eye. This distance is greater than for the normal eye.

Explanation / Answer

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a) For a lens with given refactive index, we have the following equation

nair / s + nlens / s' = nlens -  nair / R

where s is object distance , s' is image distance, R is radius

Putting in the given values,

1/36 + 1.4 /s' = 0.4 / 0.65

1/36 + 1.4/s' = 0.61538

0.61538 - 0.02777 = 1.4/s'

s' = 1.4 / 0.5876

s' = 2.3825 cm

so, distance between cornea vertex to retina is 2.3825 cm

(b) For nearsighted , the refraction occurs if distance between cornea vertex and retina is 2.60 cm. It means the distance we found is less , so This distance is shorter than for normal eye.

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