A typical human lens has an index of refraction of 1.43. The lens has a double c

Question

A typical human lens has an index of refraction of 1.43. The lens has a double convex shape, but its curvature can be varied by the ciliary 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 6.00 mm and 5.50 mm, respectively. (The numbers can vary somewhat.)

(a) If the lens were in air, what would be the ranges of its focal length and its power (in diopters)?

(b) At maximum power, where would the lens form an image of an object 25 cm in front of the front surface of the lens?
mm

minimum power D focal length at minimum power      mm maximum power D focal length at maximum power      mm

Explanation / Answer

a)

At minimum Power From Len's maker formula

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

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

f=8.721 mm

Pmin =1/0.008271 =114.67 D

At maximum power

1/f =(1.43-1)[1/6 -(-1/5.5)]

f=6.6734 mm

Pmax =1/0.0066734=149.85D

b)

From thin lens formula

1/f =1/di  +1/do

1/0.66734=1/di + 1/25

di=0.6856 cm =6.856 mm

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