Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 24, Problem 38P
To determine

The wavelengthsof +26°38',+41°08'and26°48',41°19' .

Expert Solution & Answer
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Answer to Problem 38P

First wavelength is 473nm and second wavelength is 694nm .

Explanation of Solution

Given info:

Number of grating lines per cm, N=9500lines/cm

The first order spectral lines at +26°38',+41°08'and26°48',41°19'

Formula used:

  sinθ=mλd

Where,

  m is an integer

  λ is wavelength

  d is distance between slits

Calculation:

Because the angles on each side of the central line are not the same, the incident light is not normal to the grating.

Now, calculate the average angles:

  θ1=(26°38'+26°48')2=26°43'=26.72°

  θ2=(41°08'+41°19')2=41°14'=41.23°

The path difference is an integer multiple of the wavelength in constructive interference.

Rearrange the given formula: sinθ=mλd . So, dsinθ=mλ

Now, calculate the wavelengths by using dsinθ=mλ

For angle θ=26.72°

  [1(9500lines/cm)](102m/cm)sin(26.72°)=(1)λ1λ1=4.73×107m=473nm

For angle θ=41.23°

  [1(9500lines/cm)](102m/cm)sin(41.23°)=(1)λ2λ1=6.94×107m=694nm

Conclusion:

The required wavelengths: First wavelength is 473nm and second wavelength is 694nm .

Chapter 24 Solutions

Physics: Principles with Applications

Ch. 24 - Prob. 11QCh. 24 - Prob. 12QCh. 24 - Prob. 13QCh. 24 - Prob. 14QCh. 24 - Prob. 15QCh. 24 - Prob. 16QCh. 24 - Prob. 17QCh. 24 - Prob. 18QCh. 24 - Prob. 19QCh. 24 - Prob. 20QCh. 24 - Prob. 21QCh. 24 - Prob. 22QCh. 24 - Prob. 23QCh. 24 - Prob. 24QCh. 24 - Prob. 25QCh. 24 - Prob. 26QCh. 24 - Prob. 27QCh. 24 - Prob. 28QCh. 24 - Prob. 29QCh. 24 - Prob. 30QCh. 24 - Prob. 31QCh. 24 - Prob. 32QCh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6PCh. 24 - Prob. 7PCh. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10PCh. 24 - Prob. 11PCh. 24 - Prob. 12PCh. 24 - Prob. 13PCh. 24 - Prob. 14PCh. 24 - Prob. 15PCh. 24 - Prob. 16PCh. 24 - Prob. 17PCh. 24 - Prob. 18PCh. 24 - Prob. 19PCh. 24 - Prob. 20PCh. 24 - Prob. 21PCh. 24 - Prob. 22PCh. 24 - Prob. 23PCh. 24 - Prob. 24PCh. 24 - Prob. 25PCh. 24 - Prob. 26PCh. 24 - Prob. 27PCh. 24 - Prob. 28PCh. 24 - Prob. 29PCh. 24 - Prob. 30PCh. 24 - Prob. 31PCh. 24 - Prob. 32PCh. 24 - Prob. 33PCh. 24 - Prob. 34PCh. 24 - Prob. 35PCh. 24 - Prob. 36PCh. 24 - Prob. 37PCh. 24 - Prob. 38PCh. 24 - Prob. 39PCh. 24 - Prob. 40PCh. 24 - Prob. 41PCh. 24 - Prob. 42PCh. 24 - Prob. 43PCh. 24 - Prob. 44PCh. 24 - Prob. 45PCh. 24 - Prob. 46PCh. 24 - Prob. 47PCh. 24 - Prob. 48PCh. 24 - Prob. 49PCh. 24 - Prob. 50PCh. 24 - Prob. 51PCh. 24 - Prob. 52PCh. 24 - Prob. 53PCh. 24 - Prob. 54PCh. 24 - Prob. 55PCh. 24 - Prob. 56PCh. 24 - Prob. 57PCh. 24 - Prob. 58PCh. 24 - Prob. 59PCh. 24 - Prob. 60PCh. 24 - Prob. 61PCh. 24 - Prob. 62GPCh. 24 - Prob. 63GPCh. 24 - Prob. 64GPCh. 24 - Prob. 65GPCh. 24 - Prob. 66GPCh. 24 - Prob. 67GPCh. 24 - Prob. 68GPCh. 24 - Prob. 69GPCh. 24 - Prob. 70GPCh. 24 - Prob. 71GPCh. 24 - Prob. 72GPCh. 24 - Prob. 73GPCh. 24 - Prob. 74GPCh. 24 - Prob. 75GPCh. 24 - Prob. 76GPCh. 24 - Prob. 77GPCh. 24 - Prob. 78GPCh. 24 - Prob. 79GPCh. 24 - Prob. 80GPCh. 24 - Prob. 81GPCh. 24 - Prob. 82GPCh. 24 - Prob. 83GPCh. 24 - Prob. 84GPCh. 24 - Prob. 85GPCh. 24 - Prob. 86GPCh. 24 - Prob. 87GPCh. 24 - Prob. 88GP
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