光學 CH05

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光學CH05練習題

Problem 1

Two plane waves are given by \(E_1=\frac{5E_0}{(\frac{3}{m}x-\frac{4}{s}t)^2+2}\) and \(E_2=\frac{-5E_0}{(\frac{3}{m}x+\frac{4}{s}t-6)^2+2}\)

a. Describe the motion of the two waves.

b. At what instant is their superposition everywhere zero?

c. At what point is their superposition always zero?

(b)t=___s
可嘗試次數(no. of submission)= 3

01

(c)x=___m
可嘗試次數(no. of submission)= 3

02

Problem 2

The dispersive power of glass is defined as the ratio \(\frac{n_F-n_C}{n_D-1}\) , where C, D, and F refer to the Fraunhofer wavelengths, \(\lambda_C=6563 \overset \circ A\) , \(\lambda_D=5890 \overset \circ A\) and \(\lambda_F=4861 \overset \circ A\). Find the approximate group velocity in glass whose dispersive power is \(\frac{1}{30}\) and for which \(n_D=1.50\) . (01小題)

\(v_g\)=_____m/s
可嘗試次數(no. of submission)= 3

03

Problem 3

The dispersion curve of glass can be represented approximately by Cauchy’s empirical equation, \(n=A+\frac{B}{\lambda^2}\) . Find the phase and group velocities for light of 500nm wavelength in a particular glass for which \(A=1.40\) and \(B=2.5*10^6 \overset\circ{A^2}\) . (02小題)

phase velocity \(v_p=\frac{c}{p}\)，\(p\)=_____
可嘗試次數(no. of submission)= 3

04

group velocity \(v_g=\frac{c}{g}\)，\(g\)=_____
可嘗試次數(no. of submission)= 3

05

Problem 4

Standing waves are produced by the superposition of the wave \(y=(7cm)sin[2 \pi (\frac{t}{T}-\frac{2x}{\pi cm})]\) and its reflection in a medium whose absorption is negligible. For the resultant wave, find the amplitude, wavelength, length of one loop, velocity, and period. (03小題)

the amplitude=___cm
可嘗試次數(no. of submission)= 3

06

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

07

the lengthy of one loop=_____cm
可嘗試次數(no. of submission)= 3

08

Problem 5

A certain argon-ion laser can support lasing over a frequency range of 6GHz. Estimate the number of standing wave modes that might be in the laser output if the laser cavity is 1m long. (01小題)

the number of standing wave modes=_____
可嘗試次數(no. of submission)= 3

09

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