Step-by-step explanation:
To find the distance between the second maximum of laser 1 and the third minimum of laser 2 on the same side of the central maximum, we can use the equation for the location of the maxima and minima in a double-slit interference pattern:
x = (m * λ * L) / d
Where:
x is the distance from the central maximum,
m is the order of the maxima or minima,
λ is the wavelength of the laser light,
L is the distance from the slits to the screen,
and d is the slit separation.
We can calculate the distances separately for laser 1 and laser 2 and then find the difference between them.
Given:
d is the slit separation,
L = 4.70 m,
m = 2 for the second maximum and 3 for the third minimum.
For laser 1:
λ₁ = d/20
For laser 2:
λ₂ = d/15
Calculating the distances for laser 1 and laser 2:
x₁ = (2 * (d/20) * 4.70) / d
x₂ = (3 * (d/15) * 4.70) / d
Simplifying:
x₁ = (0.235 * 4.70) / 20
x₂ = (0.705 * 4.70) / 15
x₁ = 0.05725 m
x₂ = 0.2196 m
The distance between the second maximum of laser 1 and the third minimum of laser 2 on the same side of the central maximum is the difference between these two distances:
Δx = x₂ - x₁
= 0.2196 m - 0.05725 m
= 0.16235 m
Therefore, the distance between the second maximum of laser 1 and the third minimum of laser 2 on the same side of the central maximum is approximately 0.16235 meters.