Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
1st Edition
ISBN: 9781305259836
Author: Debora M. Katz
Publisher: Cengage Learning
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Chapter 36, Problem 23PQ

(a)

To determine

The visible wavelength that will be strongly reflected.

(a)

Expert Solution
Check Mark

Answer to Problem 23PQ

The visible wavelength that will be strongly reflected is 6.50×107m.

Explanation of Solution

Write the condition for constructive interference.

    w=(m+12)λ02n

Here, w is the thickness of film, λ0 is the wavelength of the light, n is the index of refraction of oil and m is 0,1,2,3,…..

Rewrite the above equation to determine λ0.

    w=(m+12)λ02n=(2m+1)λ04nλ0=4nw2m+1                                                                                           (I)

Conclusion:

Substitute 0 for m, 1.50 for n and 325nm for w in equation (I) to calculate λ0.

    λ0=4(1.50)(325nm)2(0)+1=1950nm(109m1nm)=19.5×107m

Substitute 1 for m, 1.50 for n and 325nm for w in equation (I) to calculate λ0.

    λ0=4(1.50)(325nm)2(1)+1=650nm(109m1nm)=6.50×107m

Substitute 2 for m, 1.50 for n and 325nm for w in equation (I) to calculate λ0.

    λ0=4(1.50)(325nm)2(2)+1=390nm(109m1nm)=3.90×107m

Substitute 3 for m, 1.50 for n and 325nm for w in equation (I) to calculate λ0.

    λo=4(1.50)(325nm)2(3)+1=279nm(109m1nm)=2.79×107m

Among all four calculated wavelengths only 6.50×107 m wavelength lies in the range of visible region.

Therefore, the visible wavelength that will be strongly reflected is 6.50×107m.

(b)

To determine

The visible wavelength that will be strongly transmitted.

(b)

Expert Solution
Check Mark

Answer to Problem 23PQ

Thevisible wavelength that will be strongly transmitted is 4.88×107 m.

Explanation of Solution

Write the condition for constructive interference under transmitted light.

    w=mλ02n

Here, λ0 is the wavelength of the light, n is the index of refraction of oil and m is 0,1,2,3,…..

Rewrite the above equation to determine λ0.

    w=mλ02nλ0=2nwm                       (II)

Conclusion:

Substitute 1 for m, 1.50 for n and 325nm for w in equation (II) to calculate λ0.

    λ0=2(1.50)(325nm)1=975nm(109m1nm)=9.75×107m

Substitute 2 for m, 1.50 for n and 325nm for w in equation (II) to calculate λ0.

    λ0=2(1.50)(325nm)2=488nm(109m1nm)=4.88×107m

Substitute 3 for m, 1.50 for n and 325nm for w in equation (II) to calculate λ0.

    λ0=2(1.50)(325nm)3=325nm(109m1nm)=3.25×107m

Among all three calculated wavelengths, only 4.88×107m wavelength lies in the range of visible region.

Therefore, the visible wavelength that will be strongly transmitted is 4.88×107m.

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Chapter 36 Solutions

Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics

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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