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 5.30m away from the slits.

1.Which laser has its first maximum closer to the central maximum? Laser one or Laser 2 ?

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

3.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?

Please show work, and units.

Answer 1

The mth bright fringe occurs at position

y_m= (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 [delta_ymax - max] between the first maxima (on the same side of thecentral maximum) of the two patterns

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

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

= 0.353 m