A typical human lens has an index of refraction of 1.430. The lens has a double

Question

A typical human lens has an index of refraction of 1.430. The lens has a double convex shape, but its curvature can be varied by the culinary muscles acting around its rim. At minimum power, the radius of the front of the lens is 10.0 mm while that of the back is 6.00 mm. At maximum power the radii are 6.50 mm and 5.50 mm, respectively. If the lens were in air, what would be the maximum power and associated focal length of the lens? At maximum power, how far behind the lens would the lens form an image of an object 25.5 cm in front of the front surface of the lens?

Explanation / Answer

Part A)

Apply the lens makers equation

1/f = (n-1)(1/R1 - 1/R2)

1/f = (1.43 - 1)(1/6.5 - 1/-5.5)

f = 6.93 mm

That is .00693 m

D = 1/.00693

D = 144 Diopters

Part B)

1/f = (1.43 - 1)(1/10 - 1/-6)

f = 8.72 mm

That is .00872m

D = 1/.00872

D = 115 Diopters

Part C)

1/f = 1/p + 1/q

1/.693 = 1/25.5 + 1/q

q = .712 cm

That is .00712 m

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