Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution
Check Mark

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×105rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

    θmin=1.22λd                                                                                                     (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500nm for λ and 7.5mm for d in equation (I).

    θmin=1.22(500nm)7.5mm=1.22(500nm)(109m1nm)7.5mm(103m1mm)=8.13×105rad

Therefore, the limiting resolution of the microscope is 8.13×105rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution
Check Mark

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400nm.

Explanation of Solution

The range of the visible light is from red (λ=700nm) to violet (λ=400nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution
Check Mark

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×105rad.

Explanation of Solution

Conclusion:

Substitute 400nm for λ and 7.5mm for d in equation (I).

    θmin=1.22(400nm)7.5mm=1.22(400nm)(109m1nm)7.5mm(103m1mm)=6.51×105rad

Therefore, the angular resolution of the microscope is 6.51×105rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution
Check Mark

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×105rad.

Explanation of Solution

Conclusion:

Substitute 400nm for λ, 1.33 for n and 7.5mm for d in equation (I).

    θmin=1.22(400nm)7.5mm=1.22(400nm)(109m1nm)(1.33)7.5mm(103m1mm)=4.89×105rad

Therefore, the angular resolution of the microscope is 4.89×105rad.

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Chapter 36 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 36 - Prob. 6PQCh. 36 - Prob. 7PQCh. 36 - Prob. 8PQCh. 36 - Prob. 9PQCh. 36 - Prob. 10PQCh. 36 - Prob. 11PQCh. 36 - Prob. 12PQCh. 36 - Prob. 13PQCh. 36 - Prob. 14PQCh. 36 - Prob. 15PQCh. 36 - Prob. 16PQCh. 36 - Prob. 17PQCh. 36 - Prob. 18PQCh. 36 - Prob. 19PQCh. 36 - Prob. 20PQCh. 36 - Prob. 21PQCh. 36 - Prob. 22PQCh. 36 - Prob. 23PQCh. 36 - Prob. 24PQCh. 36 - Light of wavelength 566 nm is incident on a...Ch. 36 - Prob. 26PQCh. 36 - Prob. 27PQCh. 36 - Prob. 28PQCh. 36 - Prob. 29PQCh. 36 - Prob. 30PQCh. 36 - A light source emits a mixture of wavelengths from...Ch. 36 - Prob. 32PQCh. 36 - Prob. 33PQCh. 36 - Prob. 34PQCh. 36 - Prob. 35PQCh. 36 - Prob. 36PQCh. 36 - Prob. 37PQCh. 36 - Prob. 38PQCh. 36 - Prob. 39PQCh. 36 - Prob. 40PQCh. 36 - Prob. 41PQCh. 36 - Prob. 42PQCh. 36 - Prob. 43PQCh. 36 - Prob. 44PQCh. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - Prob. 47PQCh. 36 - Prob. 48PQCh. 36 - Problems 49 and 50 are paired. C Optical flats are...Ch. 36 - Optical flats are flat pieces of glass used to...Ch. 36 - Prob. 51PQCh. 36 - Prob. 52PQCh. 36 - Figure P36.53 shows two thin glass plates...Ch. 36 - Viewed from above, a thin film of motor oil with...Ch. 36 - Newtons rings, discovered by Isaac Newton, are an...Ch. 36 - Prob. 56PQCh. 36 - What is the radius of the beam of an argon laser...Ch. 36 - Prob. 58PQCh. 36 - A diffraction grating with 428 rulings per...Ch. 36 - How many rulings must a diffraction grating have...Ch. 36 - Prob. 61PQCh. 36 - White light is incident on a diffraction grating...Ch. 36 - X-rays incident on a crystal with planes of atoms...Ch. 36 - Prob. 64PQCh. 36 - Prob. 65PQCh. 36 - Prob. 66PQCh. 36 - The fringe width b is defined as the distance...Ch. 36 - The fringe width is defined as the distance...Ch. 36 - Prob. 69PQ
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