Question

For a normal eye, the cornea of the eye provides a converging power of $40D$ and the least converging power of the eye lens behind the cornea is $20D$. Using this information, the distance between the retina and the cornea is equal to
$\begin{aligned} & A)1.5cm \\\ & B)5cm \\\ & C)2.5cm \\\ & D)1.67cm \\\ \end{aligned}$

Answer 1

We know that focal length of the eye lens is equal to the reciprocal of effective power of the lens. Also do we know that the distance between cornea and retina is nothing but the focal length of the eye lens. Combining both these facts, we can find the focal length of eye lens with the help of effective power of the eye lens.
Formula used: $f=\dfrac{1m}{{{p}_{eff}}}=\dfrac{100cm}{{{p}_{eff}}}$

Complete answer:
We know that focal length of the eye lens is equal to the reciprocal of effective power of the lens. If $f$ represents the focal length of the eye lens, we have
$f=\dfrac{1m}{{{p}_{eff}}}=\dfrac{100cm}{{{p}_{eff}}}$
where
${{p}_{eff}}$ is the effective power of the eye lens
Let this be equation 1.
Coming to our question, we are given that the cornea of the eye provides a converging power of $40D$ and the least converging power of the eye lens behind the cornea is $20D$. Clearly, the effective power of the eye lens is given by
${{p}_{eff}}=40D+20D=60D$
Let this be equation 2.
Substituting equation 2 in equation 1, we have
$f=\dfrac{100cm}{{{p}_{eff}}}\Rightarrow f=\dfrac{100}{60}=1.67cm$
Let this be equation 3.
Here, we know that focal length of the eye lens is nothing but the distance between the retina and the cornea itself. Therefore, we can conclude that the distance between the cornea and the retina of a normal human eye is $1.67cm$.

Hence, the correct answer is option $D$.

Note:
Students need to understand that both cornea as well as the eye lens behind the same is considered as a single system. Effective power of the whole system is equal to the sum of powers of the cornea as well as that of the eye lens behind it. Retina acts as the screen of a human eye, where clear images are formed after refracting from the eye lens. Clearly, the distance between them is the focal length of the human eye lens. It should also be noted that power is calculated in $dioptre(D)$ and focal length is calculated in $cm$.