A laser with wavelength 62.5 m is shining light on a double slit with slit separ

Question

A laser with wavelength 62.5 m  is shining light on a double slit with slit separation 0.500 mm . This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits such that the fourth minimum of the first laser is at the same location as the second maximum of the second laser. What is the wavelength 2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.500 mm ?

Explanation / Answer

d is inverse of the grating constant in meters,

where m is the 1st order maxima, or the 2nd order maxima, etc.

if you want out of phase (maxima matching to minima), then m - 1/2 corresponds to the 1st minima, when m = 2

then 2 - 1/2 is the 2nd minima,

4th Minima :-

d sin? = (4 - 1/2) ?1 ...........(1)

2nd Maxima :-

d sin? = 2 ?2 ..............(2)

from (1) and (2)

2 ?2 = (4 - 1/2) ?1

2 ?2 = (4 - 1/2) d/8

?2 = 0.109 mm

2 ?2 = (4 - 1/2) ?1

2 ?2 = (4 - 1/2) d/8

?2 = 0.109 mm

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