Question

If the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect a spectacle lens of about \({\rm{16 D}}\) to be prescribed?

Short answer

The lens of the eyes contributes one-third of the eye's refractive power, hence usually a lens of high refractive power \(\left( {{\rm{16 D}}} \right)\) is prescribed to compensate for the loss of the refractive power of the eye due to the removal of the lens.

Step-by-step solution

Concept Introduction

The bending of a wave as it travels from one medium to another is known as refraction. The difference in optical density between the two substances causes bending.

Explanation for the lens

Two-thirds of the refractive power of the eye comes from the cornea, approximately the other third comes from the lens. The total refractive power of the eye, assuming an axial eye length (distance between the corneal surface to the retina)\({\rm{2}}{\rm{.35 cm}}\),is\({\rm{63}}\)dioptre. Hence, on average, the lens contributes about\({\rm{23}}\)dioptre.

Also, the person of concern might have not a perfect vision before cataract surgery, maybe he was a near-sighted person, (having an eye with a long axial length), thus the person doing cataracts might not exactly need a lens prescription of\({\rm{23}}\)dioptre but instead, a lens with less refractive power is prescribed for him.

However, in general, upon removing the lens as a procedure for cataract surgery it is quite ordinary for a lens prescription of a high dioptre to be prescribed in order to compensate for the refractive power loss due to the removal of the lens.

Calculation for the lens

According to the human anatomy - The distance between the lens and the retina is roughly \({\rm{6}}{\rm{.25 cm}}\). If the focal length of a lens is calculated with the power of \({\rm{16 D}}\), it can be obtained as,

\(\begin{aligned} f &= \frac{{{\rm{100}}}}{{{\rm{16}}\;{\rm{D}}}}\\ &= {\rm{6}}{\rm{.25 cm}}\end{aligned}\).

This proves that the lens with the power \({\rm{16 D}}\) exactly matches our anatomy.

Therefore, due to the distance between the lens and sight receptors the lens \({\rm{16 D}}\) is prescribed.