The cornea behaves as a thin lens of focal length approximately 1.80 cm , althou

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?

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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?

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Significant Figures Feedback: Your answer 19.39 mm was either rounded differently or used a different number of significant figures than required for this part.

Part C

What is the height of the image in part B?

Explanation / Answer

given

f = 1.8 cm

R1 = 5 mm = 0.5 cm

mue = 1.38

A) Apply, 1/f = (mue - 1)*(1/R1 - R2)

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

1/(1.8*0.38) = 1/0.5 - 1/R2

1/R2 = 1/0.5 - 1/1(1.8*0.38)

1/R2 = 0.538

R2 = 1.86 cm

= 18.6 mm

B) object distance, s = 25 cm

image distnace, s' = ?

Apply, 1/s + 1/s' = 1/f

1/s' = 1/f - 1/s

1/s' = 1/1.8 - 1/25

s' = 1.94 cm

= 19.4 mm

C) magnification, m = -s'/s

= -1.94/25

= -0.0776

we know, image height = m*object height

= -0.0776*15 mm

= -0.116 mm

here negative sign indicates the image inverted.

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