/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.64 A radar for tracking aircraft br... [FREE SOLUTION] | 91影视

91影视

A radar for tracking aircraft broadcasts a 12GHzmicrowave beam from a 2.0m-diameter circular radar antenna. From a wave perspective, the antenna is a circular aperture through which the microwaves diffract.

a. What is the diameter of the radar beam at a distance of 30km?

b. If the antenna emits 100kWof power, what is the average microwave intensity at 30km?

Short Answer

Expert verified

a) The diameter of the beam at a distance of 30km is915m

b) The average microwave intensity at 30km is0.152W/m2

Step by step solution

01

Radar beam (part a)

a) When a simple right triangle is constructed, the hypotenuse is the ray leading to the limit of the central maximum, that is, the beginning of the first dark circle, the catheter in front of the small angle is clearly visible. It's also important to remember that when we refer to this little angle, we're referring to its value.

tan1=RL=2L

As a consequence, we can compute our circumference in relation of both the angle as follows:

=2Ltan1

Keep in mind that we can get the angle as from darker circles criteria as

1=1.22D

=2Ltan1.22D=2Ltan1.22cDV (=c)

=23104tan1.22310821.21010V=915m

(Numerically)

02

Power and Diameter (part b)

b) We can determine the rate based on the power and diameter

I=PA=PR2=4P2

localid="1649147611891" I=411059152=0.152W/m2(Numerically)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Light of wavelength620nmilluminates a diffraction grating. The second-order maximum is at angle 39.5. How many lines per millimeter does this grating have?

A diffraction grating has slit spacing d. Fringes are viewed on a screen at distance L. Find an expression for the wavelength of light that produces a first-order fringe on the viewing screen at distanceLfrom the center of the screen.

Light from a helium-neon laser (=633nm)illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen 50cmbehind the aperture matches the diameter of the geometric image. What is the aperture's diameter (in mm)?

aFind an expression for the positions y1of the first-order fringes of a diffraction grating if the line spacing is large enough for the small-angle approximation tansinto be valid. Your expression should be in terms of d,Land.
b. Use your expression from part a to find an expression for the separationyon the screen of two fringes that differ in wavelength by.
cRather than a viewing screen, modern spectrometers use detectors-similar to the one in your digital camera-that are divided into pixels. Consider a spectrometer with a 333lines/mmgrating and a detector with 100pixels/mmlocated 12cmbehind the grating. The resolution of a spectrometer is the smallest wavelength separation minthat can be measured reliably. What is the resolution of this spectrometer for wavelengths near localid="1649156925210" 550nm, in the center of the visible spectrum? You can assume that the fringe due to one specific wavelength is narrow enough to illuminate only one column of pixels.

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0kmin diameter. Staying within this diameter is accomplished by using a special large diameter laser. If =532nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is384,000km.

See all solutions

Recommended explanations on Physics Textbooks

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.