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

Answer: a) The power of the cornea is 0.0425 diopters. b) The power of the lens is 49.9575 diopters.

Step-by-step solution

Calculate the power of the outer part of the cornea

To find the power of the outer part, we will use the lensmaker's formula: \[P = (n - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)\] For the outer part, the index of refraction (n) is 1.34, radius of curvature (R1) is 8.0 mm, and since it's a plano-convex lens, R2 is flat or infinity. So, the power of the outer part can be calculated as: \[P_\text{outer} = (1.34 - 1) \left(\frac{1}{8.0} - \frac{1}{\infty}\right)\]

Calculate the power of the inner part of the cornea

For the inner part, it's a plano-concave lens with R1 being flat (infinity) and R2 being flat as well. According to the lensmaker's formula, since both R1 and R2 are infinity, the power of the inner part is 0.

Calculate the total power of the cornea

Now, add the powers of the outer and inner parts to find the total power of the cornea: \[P_\text{cornea} = P_\text{outer} + P_\text{inner}\]

Calculate the power of the lens

Since the power of the combination of the lens and the cornea is given as 50 diopters, we can find the power of the lens by subtracting the power of the cornea from the total power: \[P_\text{lens} = P_\text{combination} - P_\text{cornea}\] Now, we will plug in the values from the previous steps and find the power of the cornea and the lens.

Plug in the values and find the answers

On step 1, we found the power of the outer part of the cornea: \[P_\text{outer} = (1.34 - 1) \left(\frac{1}{8.0} - 0\right) = 0.34 \times \frac{1}{8.0} = 0.0425~\text{diopters}\] On step 2, we found that the power of the inner part of the cornea is 0. So, the total power of the cornea is: \[P_\text{cornea} = 0.0425 + 0 = 0.0425~\text{diopters}\] Finally, we find the power of the lens: \[P_\text{lens} = 50 - 0.0425 = 49.9575~\text{diopters}\]

Answers

a) The power of the cornea is 0.0425 diopters. b) The power of the lens is 49.9575 diopters.