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 eye lens can be estimated to be.
(A) 5cm
(B) 2.5cm
(C) 1.67cm
(D) 1.5cm

Answer 1

Hint: For the given problem one should know the relation between the power and focal length of any lens. For any lens” power of that lens can be defined as the ability of the lens to converge a beam of light falling on the lens”.

Complete step by step answer:
Step 1:

It is given in the question that the power of cornea (let \[\mathop P\nolimits_1 \]) i.e., \[\mathop P\nolimits_1 = 40\]D and the power of eye lens (let \[\mathop P\nolimits_2 \]) i.e., \[\mathop P\nolimits_2 = 20D\].
We know that the total power of the combination of lenses is given by the below formula-
\[P = \mathop P\nolimits_1 + \mathop P\nolimits_2 \] …………...(1)
i.e., total power of any number of lenses in contact is equal to the algebraic sum of the powers of the individual lenses.
From the given conditions by keeping the values of both the powers in the equation (1), we get-
\[P = 40 + 20\]
\[P = 60D\]. …………...(2)

Step 2: As we know that power is the ability of the lens to converge the light beam falling on the lens and the is measured as the reciprocal of the focal length of the lens
i.e., \[P = \dfrac{{100}}{F}\]; where $F$ should be in cm.
But if there are a number of lenses are used then the focal length will be the equivalent focal length and it can be represented by \[\mathop F\nolimits_{equ} \]
So, \[P = \dfrac{{100}}{{\mathop F\nolimits_{equ} }}\] (3)
From equation (2) and (3) \[\mathop F\nolimits_{equ} \]can be calculated as given below-
\[\mathop F\nolimits_{equ} = \dfrac{{100}}{P}\]
\[\mathop F\nolimits_{equ} = 1.67\]cm.

$\therefore $ The distance between the retina and the cornea eye lens the distance between the retina and the cornea eye lens 1.67 cm. The correct option is (C).

Note:
(i) If the focal length is in meters then the relationship between power and focal length is given by \[P = \dfrac{1}{F}\]. So, while solving the problems it should be taken into account.
(ii) Here in this problem the focal length should be equal to the distance between the cornea and retina to see the image with clarity. If these both lengths are not equal then the image will not be clear