Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
5th Edition
ISBN: 9781305586871
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 27, Problem 69P

(a)

To determine

The angular resolution of VLA.

(a)

Expert Solution
Check Mark

Answer to Problem 69P

Angular resolution is 1.50arcsec.

Explanation of Solution

Write the Equation to find the wavelength.

    λ=cf

Here, c is the speed of light in vaccum, f is the freuency and λ is the wavelength.

Write the equation to find the angular resolution of VLA.

    θmin=1.22λD        (I)

Here, θmin is the angular resolution of VLA and D is the diameter of aperture.

Conclusion:

Substitute 3.00×108m/s for c and 1.40GHz for f in the equation for λ.

    λ=3.00×108m/s1.40GHz(109Hz1GHz)=0.214m

Substitute 0.214m for λ and 36.0km for D in the equation for θmin.

    θmin=1.22(0.214m36.0km(103m1km))=7.26×106rad(μrad106rad)=7.26μrad

Express the calculated value in arcsec.

    7.26μrad(180×60×60sπ)=1.50arcsec

Therefore, the angular resolution is 1.50arcsec.

(b)

To determine

The seperation between two clouds at the galaxy center.

(b)

Expert Solution
Check Mark

Answer to Problem 69P

The seperation will be 0.189ly.

Explanation of Solution

Write the equation to find the seperation between two clouds at the galaxy center.

  d=θminL

Here, d is the seperation between two clouds at the galaxy center and L is the distance to the center of galaxy.

Conclusion:

Substitute 1.50arcsec for θmin and 29,000ly for L in the above equation.

    d=(1.50arcsec(π180×60×60s))(26,000ly)=0.189ly

Therefore, the seperation will be 0.189ly.

(c)

To determine

The angular resolution of hawk’s eye.

(c)

Expert Solution
Check Mark

Answer to Problem 69P

The angular resolution is 50.8μrad.

Explanation of Solution

The given case is not correct for humans. It is assumed that hawk’s eyesight is only limited by Rayleigh’s criterion.

Conclusion:

Substitute 500nm for λ and 12.0mm for D in the equation (I).

    θmin=1.22500nm(109m1nm)12.0mm(103m1mm)=50.8×106rad(1μrad106rad)=50.8μrad

Therefore, the angular resolution is 50.8μrad.

(d)

To determine

The distance of separation between whiskers of mouse required for hawk to resolve them.

(d)

Expert Solution
Check Mark

Answer to Problem 69P

The distance of separation must be 1.52mm.

Explanation of Solution

Write the equation to find the separation between whiskers of mouse required for hawk to resolve them.

  d=θminL

Here, d is the distance of separation and L is the distance from ground to mouse.

Conclusion:

Substitute 50.8×106rad for θmin and 30.0m for L in the above equation.

    d=(50.8×106rad)(30.0m)=1.52×103m(1mm103m)=1.52mm   

Therefore, the distance of separation must be 1.52mm.

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Chapter 27 Solutions

Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)

Ch. 27 - Prob. 5OQCh. 27 - Prob. 6OQCh. 27 - A monochromatic beam of light of wavelength 500 nm...Ch. 27 - A film of oil on a puddle in a parking lot shows a...Ch. 27 - Prob. 9OQCh. 27 - A Fraunhofer diffraction pattern is produced on a...Ch. 27 - Prob. 11OQCh. 27 - Prob. 12OQCh. 27 - Why is it advantageous to use a large-diameter...Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - Prob. 3CQCh. 27 - Prob. 4CQCh. 27 - Why is the lens on a good-quality camera coated...Ch. 27 - Prob. 6CQCh. 27 - Prob. 7CQCh. 27 - Prob. 8CQCh. 27 - A laser beam is incident at a shallow angle on a...Ch. 27 - Prob. 10CQCh. 27 - Prob. 11CQCh. 27 - Prob. 12CQCh. 27 - John William Strutt, Lord Rayleigh (1842–1919),...Ch. 27 - Prob. 1PCh. 27 - Youngs double-slit experiment underlies the...Ch. 27 - Two radio antennas separated by d = 300 m as shown...Ch. 27 - Prob. 4PCh. 27 - Prob. 5PCh. 27 - Prob. 6PCh. 27 - In Figure P27.7 (not to scale), let L = 1.20 m and...Ch. 27 - Prob. 8PCh. 27 - Prob. 9PCh. 27 - Prob. 10PCh. 27 - Two slits are separated by 0.180 mm. An...Ch. 27 - Prob. 12PCh. 27 - A pair of narrow, parallel slits separated by...Ch. 27 - Coherent light rays of wavelength strike a pair...Ch. 27 - Prob. 15PCh. 27 - Prob. 16PCh. 27 - A riverside warehouse has several small doors...Ch. 27 - Prob. 18PCh. 27 - Prob. 19PCh. 27 - Astronomers observe the chromosphere of the Sun...Ch. 27 - Prob. 21PCh. 27 - Prob. 22PCh. 27 - A beam of 580-nm light passes through two closely...Ch. 27 - Prob. 24PCh. 27 - An air wedge is formed between two glass plates...Ch. 27 - Prob. 26PCh. 27 - Prob. 27PCh. 27 - Prob. 28PCh. 27 - Prob. 29PCh. 27 - Prob. 30PCh. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - A beam of monochromatic green light is diffracted...Ch. 27 - Prob. 34PCh. 27 - Prob. 35PCh. 27 - Prob. 36PCh. 27 - Prob. 37PCh. 27 - Prob. 38PCh. 27 - Prob. 39PCh. 27 - White light is spread out into its spectral...Ch. 27 - Prob. 41PCh. 27 - Prob. 42PCh. 27 - Prob. 43PCh. 27 - Prob. 44PCh. 27 - Prob. 45PCh. 27 - Prob. 46PCh. 27 - Prob. 47PCh. 27 - Prob. 48PCh. 27 - Prob. 49PCh. 27 - Prob. 50PCh. 27 - Prob. 51PCh. 27 - A wide beam of laser light with a wavelength of...Ch. 27 - Prob. 53PCh. 27 - Prob. 54PCh. 27 - Prob. 55PCh. 27 - Prob. 56PCh. 27 - Prob. 57PCh. 27 - Prob. 58PCh. 27 - Prob. 59PCh. 27 - Prob. 60PCh. 27 - Prob. 61PCh. 27 - Prob. 62PCh. 27 - Both sides of a uniform film that has index of...Ch. 27 - Prob. 64PCh. 27 - Light of wavelength 500 nm is incident normally on...Ch. 27 - Prob. 66PCh. 27 - A beam of bright red light of wavelength 654 nm...Ch. 27 - Iridescent peacock feathers are shown in Figure...Ch. 27 - Prob. 69PCh. 27 - Prob. 70PCh. 27 - Figure CQ27.4 shows an unbroken soap film in a...
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