A flat screen is located 0.43 m away from a single slit. Light with a wavelength of 530 nm (in vacuum) shines through the slit and produces a diffraction pattern. The width of the central bright fringe on the screen is 0.058 m. What is the width of the slit?
To find the width of the slit, we can use the formula for the width of the central bright fringe in a single-slit diffraction pattern:
w = (λ * D) / L
Where:
w is the width of the central bright fringe
λ is the wavelength of the light
D is the distance from the slit to the screen
L is the distance from the slit to the central maximum (bright fringe)
Given:
λ = 530 nm = 530 * 10^(-9) m (convert nanometers to meters)
D = 0.43 m
w = 0.058 m
Substituting these values into the formula, we have:
0.058 = (530 * 10^(-9) * 0.43) / L
To solve for L, we rearrange the formula:
L = (530 * 10^(-9) * 0.43) / 0.058
Using a calculator, we evaluate this expression to find:
L ≈ 3.916 m
Now that we know the value of L, we can rearrange the formula again to solve for the width of the slit (w):
w = (λ * D) / L
Substituting the known values:
w = (530 * 10^(-9) * 0.43) / 3.916
Evaluating this expression, we find:
w ≈ 5.83 * 10^(-6) m
Therefore, the width of the slit is approximately 5.83 μm (micrometers).