Double slit experiment: You set your slits 1.03 mm apart and position your screen 3.93 m from the slits. The wavelength of the laser is 631 nm. How far on the screen are the first bright fr

Question

Double slit experiment: You set your slits 1.03 mm apart and position your screen 3.93 m from the slits. The wavelength of the laser is 631 nm. How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

Answer 1

To find the positions of the first bright fringe and the second dark fringe, you can use the formula for the angular positions of fringes in a double-slit experiment:

θ = λ / d

Where:

- θ is the angle between the central maximum and the fringe.

- λ is the wavelength of the light.

- d is the distance between the slits.

First, let's calculate θ for the first bright fringe:

θ_bright = λ / d

θ_bright = (631 nm) / (1.03 mm) = 0.631/1.03 radians

Now, convert radians to degrees by multiplying by 180/π:

θ_bright = (0.631/1.03) * (180/π) degrees

θ_bright ≈ 34.86 degrees

So, the angle for the first bright fringe is approximately 34.86 degrees.

Now, let's find the position on the screen for the first bright fringe (y_bright). This position will be the distance from the central bright fringe:

y_bright = D * tan(θ_bright)

Where:

- D is the distance from the slits to the screen (3.93 m).

y_bright = (3.93 m) * tan(34.86 degrees)

Now, calculate y_bright:

y_bright ≈ 3.93 m * tan(34.86 degrees)

y_bright ≈ 3.93 m * 0.7002

y_bright ≈ 2.75 m

Now, convert meters to millimeters (1 m = 1000 mm):

y_bright ≈ 2.75 m * 1000 mm/m = 2750 mm

So, the first bright fringe is approximately 2750 millimeters (2.75 meters) from the central bright fringe on the screen.

To find the position of the second dark fringe, you can use the same approach but with θ for the second dark fringe. The second dark fringe will be at an angle of 2θ_bright from the central maximum (since dark fringes occur at angles 2θ from the central maximum in a double-slit experiment).

θ_dark = 2θ_bright

Now, calculate θ_dark:

θ_dark = 2 * 34.86 degrees = 69.72 degrees

Now, find the position on the screen for the second dark fringe (y_dark):

y_dark = D * tan(θ_dark)

y_dark ≈ (3.93 m) * tan(69.72 degrees)

Now, calculate y_dark:

y_dark ≈ 3.93 m * tan(69.72 degrees)

y_dark ≈ 3.93 m * 2.3031

y_dark ≈ 9.05 m

Now, convert meters to millimeters:

y_dark ≈ 9.05 m * 1000 mm/m = 9050 mm

So, the second dark fringe is approximately 9050 millimeters (9.05 meters) from the central bright fringe on the screen.