Two lasers are shining on a double slit, with slit separation d. Laser 1 has a w

Question

Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 6.00m away from the slits.

part A.)

Which laser has its first maximum closer to the central maximum?

part B.)

What is the distance ?ymax?max between the first maxima (on the same side of the central maximum) of the two patterns?

part C.)

What is the distance ?ymax?min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

Explanation / Answer

Well thank heavens we're talking small angles here so I don't have to document the y-values for each of these spectrum features. The small-angle approximation formula is y = m*D*lambda/d, where m is the order of the maximum (see the ref.). For a minimum of mth order you subtract 1/2*D*lambda/d.
For lambda = d/20, y(1) = 0.00026 m exactly. For lambda = d/15, y(1) = .00034666... . Now just multiply these by 1 for 1st maximum, 2 for 2nd maximum, and 2.5 for the 3rd minimum, and do the subtractions indicated. I've assumed screen distance D = 5 m, ignoring the other characters you put there. More care in question-posting would be appreciated.

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