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 5.80m away from the slits.

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

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

What is the distance delta 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.

x(1) = n ? L / d = 1 . (d/ 20) . 5.8 / d = 0.29 m

x(2) = 5.8 / 15 = 0.386 m

So distance between them is 0.096 m

b)
x(1) = 0.58 ( for the 2nd max )

x(2) = 2.5 . 0.386 = 0.965 m ( for the 3rd in )

Separation = 0.385 m

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