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Chapter 34: Q. 26 (page 991)

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

Short Answer

Expert verified

The focal length of the planoconvex polystyrene plastic lens is68cm.

Step by step solution

01

Figure for foal length of lens

Figure is,

For surfaces convex toward the object, the radius of curvatureRis positive.

For surfaces that are concave toward the object, the radius of curvature Ris negative.

02

Calculation of focal length of lens

The lens-makers' equation gives the inverse of the focal length fof a narrow lens surrounded by air.

1f=(n-1)1R1-1R2

Assuming the object is on the left, the lens's initial surface is planar, and we can think of it as a part of a sphere with.

R1鈫�鈭�

WithR2=-40, the second surface behaves as a concave surface.

Focal length is,

1f=(n-1)1R1-1R2

Substitute the following numerical values:

1f=(1.59-1)1鈭�cm-1-40cm

1f=594000cm

f=400059cm=68cm

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Most popular questions from this chapter

A concave mirror brings the sun's rays to a focus in front of the mirror. Suppose the mirror is submerged in a swimming pool but still pointed up at the sun. Will the sun's rays be focused nearer to, farther from, or at the same distance from the mirror? Explain.

A 2.0-cm-tall object is 15cmin front of a converging lens that has a20cm focal length.
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b Calculate the image position and height. Compare with your ray-tracing answers in part a.

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3. One problem with using optical fibers for communication is that a light ray passing directly down the center of the fiber takes less time to travel from one end to the other than a ray taking a longer, zig-zag path. Thus light rays starting at the same time but traveling in slightly different directions reach the end of the fiber at different times. This problem can be solved by making the refractive index of the glass change gradually from a higher value in the center to a lower value near the edges of the fiber. Explain how this reduces the difference in travel times.

A spherical mirror of radius R has its center at C, as shown in FIGURE P34.78. A ray parallel to the axis reflects through F, the focal point. Prove that f = R/2 if鈭�<<1rad.
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