A laser with wavelength d/8 is shining light on a double slit with slit separati

Question

A laser with wavelength d/8 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.

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 ?

Can you please explain specifically how the 4th minima is m+.5 and that comes to 3.5? It seems like 4th minima means m=4 so then it should be 4.5 not 3.5

Explanation / Answer

let wavelength be

1st laser
fourth minima occurs at a distance of 7a/2d

which is equal to 7a/16 as = d/8

now for 2nd laser

let wavelength be '

second maxima occurs at a distance of 2'a/d

so 7a/16 = 2'a/d

' = 7d/32 = 1.09 mm

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