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Chapter 33: Problem 52

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

Expert verified
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

01

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: \(\displaystyle \frac{1}{f} =( n-1) \cdot \frac{1}{R}\)
02

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).
03

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).

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Most popular questions from this chapter

A plastic cylinder of length \(3.0 \cdot 10^{1} \mathrm{~cm}\) has its ends ground to convex (from the rod outward) spherical surfaces, each having radius of curvature \(1.0 \cdot 10^{1} \mathrm{~cm}\). A small object is placed \(1.0 \cdot 10^{1} \mathrm{~cm}\) from the left end. How far will the image of the object lie from the right end, if the index of refraction of the plastic is \(1.5 ?\)

The object (upright arrow) in the following system has a height of \(2.5 \mathrm{~cm}\) and is placed \(5.0 \mathrm{~cm}\) away from a converging (convex) lens with a focal length of \(3.0 \mathrm{~cm}\). What is the magnification of the image? Is the image upright or inverted? Confirm your answers by ray tracing.

What is the magnification of a telescope with \(f_{0}=1.00 \cdot 10^{2} \mathrm{~cm}\) and \(f_{e}=5.00 \mathrm{~cm} ?\)

The distance from the lens (actually a combination of the cornea and the crystalline lens) to the retina at the back of the eye is \(2.0 \mathrm{~cm}\). If light is to focus on the retina, a) what is the focal length of the lens when viewing a distant object? b) what is the focal length of the lens when viewing an object \(25 \mathrm{~cm}\) away from the front of the eye?

An object of height \(h\) is placed at a distance \(d_{0}\) on the left side of a converging lens of focal length \(f\left(f
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