Light with a wavelength of 500 nm (5. 10-7 m) is incident upon a double slit with a separation of 0.44 mm (4.40 10-4 m). A screen is located 2.1 m from the double slit. At what distance from the center of the screen will the second dark fringe beyond the center fringe appear?
answer in mm
To find the distance from the center of the screen where the second dark fringe appears, we can use the formula for the location of the dark fringes in a double-slit interference pattern:
y = (m * λ * L) / d
where:
y is the distance from the center
m is the fringe order (in this case, m = 2 for the second dark fringe beyond the center)
λ is the wavelength of light (500 nm or 5.10^-7 m)
L is the distance from the double slit to the screen (2.1 m)
d is the separation between the slits (0.44 mm or 4.40. 10^-4 m)
Now we can substitute the given values into the formula:
y = (2 * 5.10^-7 m * 2.1 m) / (4.40. 10^-4 m)
Calculating this expression gives us the value of y in meters. To convert it to millimeters, we multiply by 1000 since 1 meter is equal to 1000 millimeters.
y = [(2 * 5.10^-7 m * 2.1 m) / (4.40. 10^-4 m)] * 1000
Finally, computing the expression will give us the answer in millimeters.