Homework Help: Physics help please!

Posted by Jim on Friday, March 30, 2012 at 1:23pm.

Light waves with two different wavelengths, 632 nm and 474 nm, pass simultaneously through a single slit whose width is 7.63 x 10-5 m and strike a screen 1.30 m from the slit. Two diffraction patterns are formed on the screen. What is the distance (in cm) between the common center of the diffraction patterns and the first occurrence of the spot where a dark fringe from one pattern falls on top of a dark fringe from the other pattern?

Physics help please! - Elena, Friday, March 30, 2012 at 4:39pm
Let’s use the condition of diffraction minimum for one split of the width b
b•sinα =k1•λ1
b•sinα =k2•λ2,
Since we have superposition of two maxima
b•sinα is the same for two wavelengths,
k1•λ1= k2•λ2,
λ1/λ2 = k1/k2, 632/474 = 4/3.
Therefore k1=4, k2=3.
Now
sinα = k1•λ1/b =4•632•10^-9/ 7.63•10^-5 =0.033.
As the angle is very small tanα = sinα = 0.033.
tan α= x/L,
x =L• tanα =1.3•0.033 = 0.043 m = 4/3 cm
Physics help please! - Elena, Saturday, March 31, 2012 at 6:01pm
My mistake.
It should be
k1•λ1= k2•λ2,
λ1/λ2 = k2/k1, 632/474 = 4/3.
k1 =3 k2 = 4
sinα = k1•λ1/b =3•632•10^-9/ 7.63•10^-5 =0.0248
x=L• tanα =L• sinα =1.3•0.0248 =0.0323 m = 3.23 cm

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