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

Question

The cornea behaves as a thin lens of focal length approximately 1.80cm , 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 5.00mm .
(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.) The radius of curvature of the back side of the cornea is 18.6mm.

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

B)What is the height of the image in part B?

Explanation / Answer

(A) focal length of thin lens, f = 1.8 cm

object distance, d0 = 25 cm

height of the object, h0 = 15 mm

To determine the image distance, the lens equation can be used which is given as ::

1 / di + 1 / d0 = 1 / f                                    { eq. 1 }

inserting the values in above eq.

1 / di = 1 / (1.8 cm) - 1 / (25 cm) = 23.2 / 45 cm

di = 45 / 23.2 = 1.93 cm

di = 0.0193 m

(B) height of the image hi is given as ::

hi / h0 = - di / d0                                       { eq. 2 }

inserting the values in eq.2,

hi = - ( di x h0 ) / d0                               { eq. 3 }

hi = - (0.0193 m) (15 x 10-3 ) / (0.25 m)

hi = - 1.158 mm

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