A laser with wavelength d/8 is shining light on a double slit with slit separation 0.300 mm. This results in an interference pattern on a screen a distance away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits.
(a) What is the wavelength of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.300 mm?

0.066mm

Explanation:

let wavelength be λ

1st laser

fourth minima occurs at a distance of 7λa/2d

which is equal to 7a/16 as λ = d/8

now for 2nd laser

let wavelength be λ'

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

so 7a/16 = 2λ'a/d

∴ λ' = 7d/32 = 0.066 mm

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