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Chapter 34: Q 60 (page 993)

Paraxial light rays approach a transparent sphere parallel to an optical axis passing through the center of the sphere. The rays come to a focus on the far surface of the sphere. What is the sphere鈥檚 index of refraction?

Short Answer

Expert verified

The sphere鈥檚 index of refraction is equal to 2.00

Step by step solution

01

Step 1. Given information is :Paraxial light rays approach a transparent sphere parallel to an optical axis passing through the center of the sphere .

We need to calculate the sphere鈥檚 index of refraction

02

Step 2. Using formula that is for the convex surfaces

n1s+n2s'=n2-n1Rs=鈭�asthelightraysareParaxials'=2R1鈭�+n2R=n-1.00Rn2R=n-1.00Rn2=n-1.00n=2n-2.00n=2.00

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Most popular questions from this chapter

Find the focal length of the planoconvex polystyrene plastic lens in FIGURE EX34.26.

A laser beam in air is incident on a liquid at an angle of 53鈭� with respect to the normal. The laser beam's angle in the liquid is 35鈭�. What is the liquid's index of refraction?

Shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles 胃1and 胃2in the two media. Suppose that you did not know Snell鈥檚 law.

A. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n1 and n2

B. The time depends on x. There鈥檚 one value of x for which the light travels from A to B in the shortest possible time. We鈥檒l call it xmin. Write an expression (but don鈥檛 try to solve it!) from which xmincould be found.

C. Now, by using the geometry of the figure, derive Snell鈥檚 law from your answer to part b.

You鈥檝e proven that Snell鈥檚 law is equivalent to the statement that 鈥渓ight traveling between two points follows the path that requires the shortest time.鈥� This interesting way of thinking about refraction is called Fermat鈥檚 principle.

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a Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.
bCalculate the image position and height. Compare with your ray-tracing answers in part a.

A concave mirror has a 40cmradius of curvature. How far from the mirror must an object be placed to create an upright image three times the height of the object?
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