A.A pair of narrow, parallel slits separated by a distance of 0.335 mm are illuminated by green laser light with wavelength = 543.0 nm. The interference pattern is observed on a screen 2.43 m from the plane of the parallel slits. Calculate the distance from the central maximum to the first bright region on either side of the central maximum.

B.What is the distance between the first and second dark bands in the interference pattern?

A. To calculate the distance from the central maximum to the first bright region on either side, we can use the formula for the location of the bright fringes in the double-slit interference:

y = (m * λ * L) / d

Where:
- y is the distance from the central maximum to the fringe
- m is the order of the fringe (m = 1 for the first bright fringe)
- λ is the wavelength of the light
- L is the distance from the plane of the parallel slits to the screen
- d is the distance between the slits

Plugging in the given values:
m = 1
λ = 543.0 nm = 543.0 x 10^(-9) m
L = 2.43 m
d = 0.335 mm = 0.335 x 10^(-3) m

y = (1 * 543.0 x 10^(-9) * 2.43) / (0.335 x 10^(-3))
= 0.0039 m

So, the distance from the central maximum to the first bright region on either side is approximately 0.0039 m.

B. The distance between the first and second dark bands can be calculated using the same formula. However, since we are looking for the dark bands, we need to adjust the formula by including an additional factor of 1/2. The formula becomes:

y = (m + 1/2) * λ * L / d

Plugging in the values:
m = 1
λ = 543.0 nm = 543.0 x 10^(-9) m
L = 2.43 m
d = 0.335 mm = 0.335 x 10^(-3) m

y = (1 + 1/2) * 543.0 x 10^(-9) * 2.43 / (0.335 x 10^(-3))
= 0.0070 m

So, the distance between the first and second dark bands in the interference pattern is approximately 0.0070 m.

To solve A and B, we can use the formula for the distance between two consecutive bright or dark fringes in an interference pattern:

Distance between fringes = (wavelength * distance to screen) / (distance between slits)

Let's plug in the given values to calculate the answers:

A. To find the distance from the central maximum to the first bright region on either side of the central maximum:

Given:
Wavelength (λ) = 543.0 nm = 543.0 × 10^(-9) m
Distance between slits (d) = 0.335 mm = 0.335 × 10^(-3) m
Distance to screen (D) = 2.43 m

Distance between fringes = (wavelength * distance to screen) / (distance between slits)
= (543.0 × 10^(-9) m * 2.43 m) / (0.335 × 10^(-3) m)
= 3.945 m

Therefore, the distance from the central maximum to the first bright region on either side of the central maximum is 3.945 m.

B. To find the distance between the first and second dark bands in the interference pattern:

The distance between the first and second dark bands is the same as the distance between two consecutive bright fringes.

So, we can use the same formula as in question A:

Distance between fringes = (wavelength * distance to screen) / (distance between slits)
= (543.0 × 10^(-9) m * 2.43 m) / (0.335 × 10^(-3) m)
= 3.945 m

Therefore, the distance between the first and second dark bands in the interference pattern is also 3.945 m.