Monochromatic light with a wavelength of 5.0 E -7 meter passes through two narrow slits, producing an interference pattern on a screen 3.0 meters away. The first order bright band lines 2.0 E -2 meters away from the central bright maxima. What is the distance between the slits?

There are bright bands where

x = m (lambda)D/d

d is the slit separation (which is what you want to solve for).

x = distance from central bright band to first order maximum = 0.02 m
m = 1 for first order interference
D = distance to screen = 3.0 m
lambda = wavelength = 5*10^-7 m

Solve for d

To find the distance between the slits, we can use the formula for the location of bright fringes in a double-slit interference pattern:

y = (λ * L) / d

Where:
y = distance from the central bright maxima
λ = wavelength of the light
L = distance between the slits and the screen
d = distance between the slits

We are given:
λ = 5.0 E -7 meter
L = 3.0 meters
y = 2.0 E -2 meters

Rearranging the formula to solve for d:

d = (λ * L) / y

Substituting the given values:

d = (5.0 E -7 meter * 3.0 meters) / (2.0 E -2 meters)

Simplifying:

d = (1.5 E -6 meter * meters) / (0.02 meters)

d = 75 E -6 meter

Therefore, the distance between the slits is 75.0 E -6 meter.

To find the distance between the slits, we can use the equation for the interference pattern:

y = (λ * L) / d

where:
- y is the distance from the central bright maximum to the first-order bright band,
- λ is the wavelength of the light,
- L is the distance between the slits and the screen,
- d is the distance between the slits.

In this case, we know the following values:
- y = 2.0 E -2 meters
- λ = 5.0 E -7 meter
- L = 3.0 meters

Let's rearrange the equation to isolate the distance between the slits (d):

d = (λ * L) / y

Substituting the known values:

d = (5.0 E -7 meter * 3.0 meters) / (2.0 E -2 meters)
d = (1.5 E -6 meter * meters) / (2.0 E -2 meters)
d = 1.5 E -6 / 2.0 E -2 meter

Simplifying:

d = (1.5 / 2.0) E -6 / E -2 meter
d = 0.75 E -6 * E 2 meter
d = 0.75 E -6+2 meter
d = 0.75 E -4 meter

Therefore, the distance between the slits is 0.75 E -4 meters.