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

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force