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 4.70 m away from the slits. What is the distance between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

Answer 1

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.