Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 35: Q. 28 (page 1018)

A common optical instrument in a laser laboratory is a beam expander. one type of beam expander is shown in FIGURE P35.28.

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

the right?

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

Short Answer

Expert verified

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

b. The width of the exiting laser beam isω2=f2f1ω1.

Step by step solution

01

part(a) Step 1: Given information

We need to find what lens spacing d does a parallel laser beam exit from the right.

02

part(a) Step 2: Explanation

We find this distance as the sum of the focal length of the first lens and the focal length of the second lens:

d=f1+f2

03

part (b) step 1: Given Information

We need to find the width of the exiting laser beam.

04

part (b) step 2: Simplification

let us find width ω2,

ω2ω1=f2f1ω2f1=ω1f1ω2=f2f1ω1

Here, ω1is the width of the first lens,ω2is the width of the second lens, role="math" localid="1650107475863" f1andf2is the focal length of first lens and second lens.

05

part (b) step 3: Diagram

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

what is the f-numberof a relaxed eye with the pupil fully dilated to localid="1648735653936" 8.0mm? model the eye as a single lens localid="1648735646217" 2.4cmin front of the retina.

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.

Two light bulbs are 1.0mapart. from, what distance can these light bulbs be marginally resolved by a small telescope with a 4.0-cm-diameterobjective lens? assume that the lens is diffraction limited andλ=600nm.

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 600 nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)

The lens shown in FIGURE CP35.49 is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R.

a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is f=R/12n2-n1-12, where localid="1648757054673" n1and n2are, respectively, the indices of refraction of the diverging and the converging lenses. Don’t forget to make the thin-lens approximation.

b. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define ∆n1 and ∆n2 as nblue-nred for the two lenses. What value of the ratio ∆n1/∆n2makes fblue=fredfor the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.

c. Indices of refraction for two types of glass are given in the table. To make an achromatic doublet, which glass should you use for the converging lens and which for the diverging lens? Explain

nblue nred

Crown glass 1.525 1.517

Flint glass 1.632 1.616

d. What value of R gives a focal length of 10.0cm?
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Electrostatics

Read Explanation

Rotational Dynamics

Read Explanation

Turning Points in Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Energy Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free