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Chapter 35: Q. 29 (page 1018)

A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P 35.29. The parallel rays of a laser beam of width w1 enter from the left.

a. For what lens spacing d does a parallel laser beam exit from the right?

b. What is the width w2 of the exiting laser beam?

Short Answer

Expert verified

a. Lens spacing d does a parallel laser beam exit from the right d=f2+f1.

b. The width w2 of the exiting laser beam isw2=f2f1w2.

Step by step solution

01

Part (a) Step 1: Given Information.

We need to find out d's lens spacing a parallel leaser beam exit from the right.

02

Part (b) Step 2: Diagram explanation.

We see the following from the picture which is given below:

d=f2-f1

If f1<0, which is equivalent to:

d=f2+f1

Here, dis the distance between lens, f1andf2is the focal length of the first and second lens respectively.

03

Part(b) Step 1: Given Information.

We need to find out the width w2leaser beam.

04

Part (b) Step 2: Explanation.

As we know that to find width w2

Triangles a from above picture, we can get the values for w2:

w1f1=w2f2鈬�w2=f2f1w1

Here, w1andw2is the width of first lens and second lens and f1,f2are the focal length of first and second lens respectively.

So, if is f2>f1and our conclusion show that is w2>w1.

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Most popular questions from this chapter

White light is incident onto a 30掳prism at the 40掳angleshown in Figure p35.41. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is 20%larger than the index of refraction of red light. At what angle蠒does red light emerges from the rear face?

Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you鈥檙e farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power +4.5Dand your right eye鈥檚 lens is +3.0D. a. Which lens should you use for the objective and which for the eyepiece? Explain.

b. What will be the magnification of your telescope?

c. How far apart should the two lenses be when you focus on distant objects?

A camera takes a properly exposed photo with a 3mmdiameter aperture and a shutter speed of 1/125s.. What is the appropriate aperture diameter for a 1/1500sshutter speed?

FIGURE CP35.50shows a simple zoom lens in which the magnitudes of both focal lengths are f. If the spacing d<f, the image of the converging lens falls on the right side of the diverging lens. Our procedure of letting the image of the first lens act as the object of the second lens will continue to work in this case if we use a negative object distance for the second lens. This is called a virtual object. Consider an object very far to the left (s鈮�鈭�)of the converging lens. Define the effective focal length as the distance from the midpoint between the lenses to the final image.

a. Show that the effective focal length is

feff=f2-fd+12d2d

b. What is the zoom for a lens that can be adjusted from d=12fto d=14f?

The resolution of a digital cameras is limited by two factors diffraction by the lens, a limit of any optical system, and the fact that the sensor is divided into discrete pixels. consirer a typical point-and--shoot camera that has a 20-mm-focal-lengthlens and a sensor with 2.5-渭m-widepixels.

(a) . First, assume an ideal, diffractionless lens, at a distance of 100m,what is the smallest distance, in cmbetween two point sources of light that the camera can barely resolve? in answering this question, consider what has to happen on the sensor to show two image points rather than one you can use S1=fbecauses>>f.

(b) . You can achieve the pixel-limied resolution of part a only if the diffraction which of each image point no greater than the diffraction width of image point is no greater than 1pixel in diameter. for what lens diameter is the minimum spot size equal to the width of a pixel ? use 600nmfor the wavelength of light.

(c). what is the f-numberof the lens for the diameter you found in part b? your answer is a quite realistic value of the f-numberat which a camera transitions from being pixel limited to being diffraction limited for f-numbersmaller than this (larger-diameter apertures), the resolution is limited by the pixel size and does not change as you change the apertures. for f-numberlarger than this (smaller-diameter apertures). the resolution is limited by diffraction and it gets worse as you "stop down" to smaller apertures.
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