Question

The uncorrected far point of Charlotte's eye is 2.1 m. What refractive power contact lens enables her to clearly distinguish objects at large distances? Assume that the distance from the cornea-lens system to the retina is 2.0 cm and the normal near point is 28 cm.

Answer 1

Measurements in metres.
Real is positive sign convention.
f[f] = focal length of eye lens at farpoint,
f[n] = focal length of eye lens at nearpoint,
f[l] = focal length of contact lens.
x = distance of nearpoint without contact lens.

Without contact lenses:
1 / 2.1 + 1 / 0.020 = 1 / f[f] ...(1)
1 / x + 1 / 0.020 = 1 / f[n] ...(2)

With contact lenses:
0 + 1 / 0.020 = 1 / f[f] + 1 / f[l] ...(3)
1 / 0.28 + 1 / 0.020 = 1 / f[n] + 1 / f[l] ...(4)

Subtracting (1) from (3):
1 / f[l] = - 10 / 21
Power = 0.5 dioptre (diverging).

Subtracting (4) from (2):
1 / x - 1 / 0.28 = - 1 / f[l] = 10 / 20
x = ans in cm.

Uncorrected nearpoint is ans cm.