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. 1. Which laser has its first maximum closer to the central maximum?
2. What is the distance Δymax--max between the first maxima (on the same side of the central maximum) of the two patterns?
3. What is the distance Δymax-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

1) aser 1 has the maximum closest to the center

2)  Δy = 0.0866 m ,   3)   Δy = 0.693 m

Explanation:

The interference phenomenon is described by the expression

         d sin θ = m λ                    for constructive interference

         d sin θ = (m + ½) λ           for destructive interference

We can use trigonometry to find the angle

        tan θ = y / L

in trigonometry experiments the angles are small

        tam θ =

        sin θ = y / L

we substitute

         d y / L = m λ       (1)

1) Let's find the first maximum that corresponds to m = 1 for each laser

   laser 1    λ = d / 20

        d y₁ / L = 1 d / 20

        y₁ = L / 20

        y₁ = 5.20 / 20

        y₁ = 0.26 m

Laser 2      λ= d / 15

         d y₂ / L = 1 d / 15

         y₂ = d / 15

         y₂ = 5.20 / 15

         y₂ = 0.346 m

Therefore laser 1 has the maximum closest to the center

2) the difference between these maxima

       Δy = y₂ - y₁

       Δy = 0.3466 - 0.26

       Δy = 0.0866 m

3) we look for the second maximum m = 2 of laser 1, we substitute in equation 1

         y₃ = 2 5.20 / 20

         y₃ = 0.52 m

now let's find the third minimum m = 3 of laser 2

         d y₄ / L = (m + ½) λ

         d y₄ / 5.20 = (3 + ½) d / 15

         y₄ = 3.5 5.20 / 15

         y₄ = 1.213 m

        Δy = y₄ -y₃

        Δy = 1.213 - 0.52

        Δy = 0.693 m

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