The lens at the front of your eye must produce a sharp image

The lens at the front of your eye must produce a sharp image in on your retina, at the back of your eyeball. If your vision is good, it can do this whether the object is 1 foot or 100 yards away. Estimate the range of focal lengths that a \"good\" eye can adopt. Your eye is approximately a sphere with a diameter of 1 inch.

Solution

consider the lens equation

1/d_o+ 1/d_i = 1/f

d_o ranges from 1 foot to 100 yds and d_i is the diameter of the eye, more precisely, the distance between lens and retina[ diameter is about 24 millimetres (about one inch)]

when d₀= 1foot=0.305 m

d_i=1inch=0.0254 m

1/d_o+ 1/d_i = 1/f₁

1/0.305 +1/0.0254= 1/f₁

f₁=0.023 m

when d₀= 100 yards=91.44 m

d_i=1inch=0.0254 m

1/d_o+ 1/d_i = 1/f₂

1/91.44 +1/0.0254= 1/f₂

f₂=0.0254 m

here the focal length ranges from f₁ [0.023m] to f₂ [0.0254m]