Question

The cornea behaves as a thin lens of focal length approximately 1.80 cm , although this varies a bit. The material of which it is made has an index of refraction of 1.38, and its front surface is convex, with a radius of curvature of 5.00 mm .

(Note: The results obtained here are not strictly accurate, because, on one side, the cornea has a fluid with a refractive index different from that of air.)

Part A: If this focal length is in air, what is the radius of curvature of the back side of the cornea?

Part B: The closest distance at which a typical person can focus on an object (called the near point) is about 25.0 cm , although this varies considerably with age. Where would the cornea focus the image of an 15.0 mm -tall object at the near point?

Part C: What is the height of the image in part B?

Part D: Is this image real or virtual? Is it erect or inverted?

Answer 1

from lens makers equation

1/F = (n1/n2 - 1) *( 1/R1 - 1/R2)

F = 1.8 cm

n1 = 1.38

n2 = air = 1

R1 = 5 mm = 0.5 cm

1/1.8 = (1.38-1)*(1/0.5-1/R2)

R2 = 1.86 cm = 18.6 mm

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part(B)

1/s + 1/s' = 1/f

s = 25 cm

f = 1.8 cm

1/25 + 1/s' = 1/1.8

s' = 1.94 cm

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(C)

magnification lMl = s'/s = -hi/ho

1.94/25 = hi/15

height of the image = 1.164

(D)

s' = +ve the image is real

magnification M = -s's/ = -ve indicatede the image is inverted