光學 CH07

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光學CH07練習題

Problem 1

Two mutually coherent beams having parallel electric fields are described by

\(E_1=3cos(ks_1-\omega t +\frac{\pi}{5})\)

\(E_2=4cos(ks_2-\omega t +\frac{\pi}{6})\)

with amplitudes in kV/m. The beams interfere at a point P where the phase difference due to path is \(\pi/3\) (the first beam having the longer path). At the point of superposition, calculate (a) the irradiances \(I_1\) and \(I_2\) of the individual beams; (b) the irradiance \(I_{12}\) due to their interference;(c) the net irradiance; (d) the fringe visibility.

(a)\(I_1\)=______\(W/m^2\)
可嘗試次數(no. of submission)= 3

01

(a)\(I_2\)=______\(W/m^2\)
可嘗試次數(no. of submission)= 3

02

(b)\(I_{12}\)=______\(W/m^2\)
可嘗試次數(no. of submission)= 3

03

(c)\(I\)=______\(W/m^2\)
可嘗試次數(no. of submission)= 3

04

(d)visibility=______
可嘗試次數(no. of submission)= 3

05

Problem 2

Two harmonic light waves with amplitudes of 1.6 and 2.8 interfere at some point P on a screen. What visibility results there if (a) their electric field vectors are parallel and (b) if they are perpendicular? (02小題)

(a)for parallel field, visibility=_____
可嘗試次數(no. of submission)= 3

06

(b)for perpendicular field, visibility=_____
可嘗試次數(no. of submission)= 3

07

Problem 3

The ratio of the amplitudes of two beams forming an interference fringe pattern is 2/1. What is the visibility? What ratio of amplitudes produces a visibility of 0.5? (02小題)

the visibility=_____
可嘗試次數(no. of submission)= 3

08

the ratio of amplitudesthe=_____
可嘗試次數(no. of submission)= 3

09

Problem 4

Two slits are illuminated by light that consists of two wavelength. One wavelength is known to be 436nm. One a screen, the forth minimum of the 436-nm light coincides with the third maximum of the other light. What is the wavelength of the other light? (01小題)

the wavelength=_____nm
可嘗試次數(no. of submission)= 3

10

Problem 5

In a Young’s experiment, narrow double slits 0.2nm apart diffract monochromatic light onto a screen 1.5m away. The distance between the fifth minima on either side of the zeroth-order maximum is measured to be 34.73mm. Determine the wavelength of the light.

the wavelength=_____nm
可嘗試次數(no. of submission)= 3

11

Problem 6

A nonreflecting, single layer of a lens coating to be deposited on a lens of refractive index \(n=1.78\). Determine the refractive index of a coating material and thickness required to produce zero reflection for light of wavelength \(550nm\). (02小題)

the refractive index=_____
可嘗試次數(no. of submission)= 3

12

the thickness=_____nm
可嘗試次數(no. of submission)= 3

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Problem 7

A fringe pattern, such as that in the figure, found using an interference microscope objective, is observed to have a regular spacing of 1mm. At a certain point in the pattern, the fringes are observed to shift laterally by 3.4mm. If the illumination is green light of 546.1nm, what is the dimension of the “step” in the film that caused the shift?

______nm
可嘗試次數(no. of submission)= 3

14

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