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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 P35.29.

The parallel ray of a laser beam of width ω1enter from the left.

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

b. What is the width ω2of the exiting laser beam?

Short Answer

Expert verified

a.)d-f2+f1

b.)ω2-f2

Step by step solution

01

Step.1 Given information

a.)From the given values shown in FIGURE

d=f2-f1

If f1<0,this equationto

02

Step 2. Explanation

b.) we need to find width ω2

From triangles picture, we get Value of ω2

ω1f1=ω2f2

⇒ω2=f2f1ω1

So, if isf2>f1and our answer then shows is ω2>ω1

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Most popular questions from this chapter

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-μm-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.

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≈∞)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?

To focus parallel light rays to the smallest possible spot, should you use a lens with a small f-number or a large f-number? Explain.

Two converging lenses with focal lengths of 40cmand 20cmare 10cmapart. A 2.0cmtall object is 15cmin front of the40cmfocal-length lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Yang can focus on objects 150cm away with a relaxed eye. With full accommodation, she can focus on objects 20cmaway. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?

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