Two lasers are shining on a double slit, with slit separationd. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patternson a screen a distance 5.00 {/rm m} away from the slits.

Part A

Which laser has its first maximum closer to the centralmaximum?

Part B

What is the distance Deltay_max-max between the first maxima (on the same side of thecentral maximum) of the two patterns?

Part B. 1

Find the location of the first maximum for laser1

Part B. 2

Find the location of the first maximum for laser2Part C

What is the distance Deltay_max-min between the second maximum of laser 1 and the thirdminimum of laser 2, on the same side of the central maximum?

a) laser 1 has the maximum closest to the central maximum

b) y₂ - y₁ = L 1.66 10⁻²

Explanation:

a), B1, B2) The expression that describes the constructive interference for a double slit is

d sin θ = m λ

The pattern is observed on a screen

tan θ = y / L

Since the angles are very small

tan θ = sin θ / cos θ = sin θ = y/L

d y / L = m λ

In this case the laser has a wavelength

λ ₁ = d/20

We substitute

d y / L = m d / 20

m = 1

y₁ = L / 20

For the laser 2 λ ₂ = d / 15

y₂ = L / 15

When examining the two expressions, laser 1 has the maximum closest to the central maximum

b) the difference between the two patterns is

y₂ - y₁ = L (1/15 - 1/20)

y₂ - y₁ = L 1.66 10⁻²

C) laser 1 second maximum

y₁ ' = 2 L / 20

y₁ ' = L 0.1

Laser 2 third minimum

To have a minimum, the equation must be satisfied

d sin θ = (m + ½) λ

d y / L = (m + ½) λ

d y / L = (m + ½) d / 15

y = L (m + 1/2) / 15

m = 3

y₂' = L (3 + ½) / 15

y₂' = L 0.2333

The difference is

y₁ ' - y₂' = L (0.1 - 0.2333)

y₁ '-y₂' = L (-0.133)