91Ó°ÊÓ

Geometrical optics describes that light propagates as rays. Rays are approximate paths along which light propagates under specific circumstances such as homogeneous medium.

An optical lens is a transparent transmissive optical component that is used to either converge or diverge the light emitting from a object. These transmitted light forms an image of that object.

Object-image relationship for spherical reflecting surface:

$\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R}$

Here,

n₁ and n₂ are refractive indices of both the surfaces

u = object distance from the vertex of spherical surface

v = image distance from the vertex of spherical surface

R = Radius of the spherical surface

Sign Convention:

1. Object Distance (u): (+) in front of lens; (-) in the back of lens
2. Image Distance (v): (-) in front of lens; (+) in the back of lens
3. Radius of curvature (R): (+) for center of curvature on same side of outgoing light; (-) for center of curvature on other side of outgoing light.

We have given,

Object distance,

Image distance,

$n_1=1$ (for air)

$n_2=1.4$ (medium inside eye)

By using Object-image relationship for spherical reflecting surface:

$$\begin{gathered} ⇒\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R} \\ ⇒\frac{1}{+40}+\frac{1.4}{+2.6}=\frac{1.4-1}{R} \\ ⇒\frac{0.4}{R}=\frac{2.6+56}{40*2.6} \\ ⇒R=0.71cm \end{gathered}$$

Therefore, the radius of curvature of the cornea is 0.71 cm .