CLASS EXERCISE #21 - 26 July 2005
Laser light of wavelength - passes through two slits onto a screen. The slits
each have width + and the separation between the centers of the two slits is six
times as large: . œ 6+.
What is the smallest value of sin ) (in terms of -ß .ß and +) for an angle
)  0 where an interference maximum appears to be missing because it
coincides with a diffraction minimum?
Which interference maxima appear to be missing (for example, the 3rd, 5th,
7th, etc.)?
Explain in words your reasoning and the formulas you are using to show this.
The interference maxima occur for . sin ) œ 7- or
sin ) œ 7-Î. œ 7-Î6+ for 7 œ 0, 1, 2, 3, etc.
or
sin ) œ -Î6+, 2-Î6+, 3-Î6+, 4-Î6+ß 5-Î6+, 6-Î6+,
7 - Î 6 + , 8- Î 6+ , . . .
The diffraction minima occur for + sin ) œ 7w - or
sin ) œ 7w -Î+ for 7w œ 1, 2, 3, etc.
or
sin ) œ -Î+, 2-Î+, 3-Î+, 4-Î+, 5-Î+, 6-Î+, . . .
The smallest value of sin ) that occurs on both these lists is
sin ) œ -Î+
corresponding to the first diffraction minimum and the sixth interference maximum
(not counting the central maximum). The sixth interference maximum will then be
missing.
More generally an interference maximum coincides with a diffraction
minimum when 7-Î6+ œ 7w -Î+ or 7 œ 67w , or for 7 œ 6, 12, 18, . . . (every
6th interference maximum).