By using the formula for the position of fringes in a double-slit interference pattern and the given information, we were able to calculate the separation of the two slits to be approximately 0.328 mm.
Let's solve this step-by-step:
1. Given Information:
Wavelength of light (λ) = 656 nm = 656 x 10^-9 m
Distance of third-order fringe from the center (y_3rd) = 32 mm = 0.032 m
Distance from slits to screen (D) = 1.6 m
2. Formula:
The position of the nth bright fringe in a double-slit interference pattern is given by:
y_n = nλD / d
where:
n is the order of the fringe (n = 1 for the first bright fringe, n = 2 for the second bright fringe, and so on)
λ is the wavelength of light
D is the distance from the slits to the screen
d is the separation of the two slits
3. Solving for d:
We are interested in the separation of the slits (d). We can rearrange the formula above to solve for d:
d = nλD / y_n
Plugging in the known values:
d = 3 * 656 x 10^-9 m * 1.6 m / 0.032 m
d ≈ 0.000328 m = 0.328 mm
Therefore, the separation of the two slits is approximately 0.328 mm.
4. Visualizing the Interference Pattern:
Doubleslit interference pattern
The diagram above shows a typical double-slit interference pattern. The central fringe is the brightest spot, and the intensity of the fringes decreases as we move away from the center. The separation between the fringes depends on the wavelength of light and the separation of the slits.
Conclusion:
By using the formula for the position of fringes in a double-slit interference pattern and the given information, we were able to calculate the separation of the two slits to be approximately 0.328 mm.