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

Question

1) 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 5.20m away from the slits.

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

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

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

The mth bright fringe occurs at position

ym= (m * lambda * L/d) [m =0,1,2,3,...........]

The interference pattern is symmetrical,so there is an mthbright fringe at the same distance on both sides of thecenter.

the distance of the first maximum for the first laser is

y1= (1 * lambda1 * L/d)

lambda1 = (d/20) , L = 5.30 m

y1= (1 * (d/20) * 5.30/d) = 0.265 m

The distance of the first maximum for the second laser is

y1'= (1 * lambda2 * L/d)

lambda2 = (d/15)

y1' = (1 * (d/15) * 5.30 / d) = 0.353 m

The first laser has its first maximum closer to the central maximum

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The distance [deltaymax - max] between the first maxima (on the same side of thecentral maximum) of the two patterns

[deltaymax - max] = y1' - y1 = 0.353 - 0.265

= 0.088 m

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The second maximum of laser 1 is

y2 = (2 * lambda1 * L/d) = (2 * (d/20) * 5.30/d) = 0.53 m

The third minimum of laser 2 is

y3' = (3 + (1/2)) * ( lambda2 * L/d) = ((5/2) * lambda2 * L/d)

y3' = (2.5 * (d/15) * 5.30/d)

= 0.883 m

the distance [deltaymax - min] between the second maximum of laser 1 and the thirdminimum of laser 2, on the same side of the central maximum

[deltaymax - min] = y3' - y2 = 0.883 - 0.53

= 0.353 m

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