Question

The radius of curvature for the outer part of the cornea is \(8.0 \mathrm{~mm}\), the inner portion is relatively flat. If the index of refraction of the cornea and the aqueous humor is 1.34: a) Find the power of the cornea. b) If the combination of the lens and the cornea has a power of \(50 .\) diopter, find the power of the lens (assume the two are touching).

Short answer

Question: Given the radius of curvature for the outer part of the cornea as R = 8.0 mm and the index of refraction of the cornea and aqueous humor as n = 1.34, find the optical power of the cornea and the power of the lens. The combination of lens and cornea has a power of 50 D. Answer: The optical power of the cornea is approximately 11.2 D and the power of the lens is approximately 38.8 D.

Step-by-step solution

Recall the lens maker's formula

The lens maker's formula relates the focal length \(\displaystyle f\) of a thin lens to its radius of curvature \(\displaystyle R\) and the index of refraction \(\displaystyle n\). The formula is given by: \(\displaystyle \frac{1}{f} =( n-1) \cdot \frac{1}{R}\)

Calculate the power of the cornea

To find the power of the cornea, we need to calculate the focal length using the lens maker's formula. Given the radius of curvature \(\displaystyle R\ =\ 8.0\ \mathrm{mm}\) and the index of refraction \(\displaystyle n\ =\ 1.34\), we can find the focal length \(\displaystyle f\) as follows: \(\displaystyle \frac{1}{f} =( 1.34-1) \cdot \frac{1}{8.0}\) Now, solve for the focal length \(\displaystyle f\). After finding \(\displaystyle f\), we can calculate the power of the cornea as the inverse of the focal length (in meters). We will express the power in diopters (D).

Calculate the power of the lens

To find the power of the lens, we will use the given information about the combined power of the lens and cornea. The combination of lens and cornea has a power of \(\displaystyle 50\ \mathrm{D}\). Since the power of a lens system is the sum of the individual powers, the power of the lens can be found using the following equation: \(\displaystyle P_{\text{lens}} =P_{\text{total}} -P_{\text{cornea}}\) Now, plug in the values of the total power and the power of the cornea. After finding the power of the lens, express it in diopters (D).