Coherent light of frequency 6.38×1014 Hz passes through two thin slits and falls on a screen 80.0 cm away. You observe that the third bright fringe occurs at ± 3.08 cm on either side of the central bright fringe.

Question

How far apart are the two slits?
At what distance from the central bright fringe will the third dark fringe occur?

Answer 1

We can use the equation for the location of the bright fringes in a double-slit experiment:

y = (mλL) / d

where y is the distance from the central bright fringe to the m-th bright fringe on the screen, λ is the wavelength of the light, L is the distance from the slits to the screen, d is the distance between the two slits, and m is an integer representing the order of the bright fringe.

To find the distance between the slits, we can rearrange the equation to solve for d:

d = (mλL) / y

Using the given values, we can solve for d:

λ = 3.00 × 10^8 m/s / 6.38 × 10^14 Hz = 4.69 × 10^-7 m
L = 80.0 cm = 0.8 m
m = 3
y = 3.08 cm = 0.0308 m

d = (mλL) / y = (3)(4.69 × 10^-7 m)(0.8 m) / 0.0308 m = 3.86 × 10^-6 m

Therefore, the distance between the two slits is approximately 3.86 micrometers.

To find the location of the third dark fringe, we can use the equation:

y = [(2m + 1)λL] / (2d)

where m is an integer representing the order of the dark fringe.

We want to find the distance from the central bright fringe to the third dark fringe, so we can set m = 1:

y = [(2 × 1 + 1)λL] / (2d) = (3λL) / (2d)

Using the values we calculated earlier:

y = (3)(4.69 × 10^-7 m)(0.8 m) / (2)(3.86 × 10^-6 m) = 0.244 m

Therefore, the third dark fringe is located 0.244 meters away from the central bright fringe.

Answer 2

Note: It's important to keep track of units when using these equations. In our calculations, we converted the given values to SI units (meters) and made sure the final answers were also in meters.