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

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 5.10m  away from the slits.

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? Express your answer in meters. 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 5.10m  away from the slits.

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? Express your answer in meters.

Explanation / Answer

The small-angle approximation formula is y = m*D*lambda/d,

where m is the order of the maximum . For a minimum of mth order you subtract 1/2*D*lambda/d.
For lambda = d/20, y(1) = 5.1*d/20/d = 0.255 m exactly. For lambda = d/15, y(1) = 0.34 m

for 2nd max of 1st laser y = 2*(0.255) m = 0.51 m

for 3rd min of 2nd laser y = (3- 1/2)*(0.34) = 0.85 m

difference = 0.85 m - 0.51 m = 0.34 m

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