To find the width of the central maximum, we can use the equation:
w = (2 * λ * D) / a
Where:
- w is the width of the central maximum
- λ is the wavelength of the helium-neon laser light (632.8 nm or 6.328 × 10^-7 m)
- D is the distance between the slit and the screen (3.00 m)
- a is the width of the single slit (0.330 mm or 0.00033 m)
Plugging in the values, we get:
w = (2 * 6.328 × 10^-7 m * 3.00 m) / 0.00033 m
w = 0.00573 m
Therefore, the width of the central maximum on the screen is approximately 0.00573 meters.
Hello! I'd be happy to help you with your question. To find the width of the central maximum on the screen, we'll use the formula for the angular width of the central maximum in a single-slit diffraction pattern:
θ = 2 * (λ / a)
Where θ is the angular width, λ is the wavelength of the laser light (632.8 nm), and a is the width of the single slit (0.330 mm).
First, let's convert the given units to meters:
λ = 632.8 nm * (1 m / 1,000,000,000 nm) = 6.328e-7 m
a = 0.330 mm * (1 m / 1000 mm) = 3.30e-4 m
Now, plug the values into the formula:
θ = 2 * (6.328e-7 m / 3.30e-4 m) = 3.835e-3 radians
To find the width of the central maximum (W) on the screen, we'll use the formula:
W = L * tan(θ/2)
Where L is the distance from the slit to the screen (3.00 m).
W = 3.00 m * tan(3.835e-3 radians / 2) = 0.005767 m
Convert the result to millimeters:
W = 0.005767 m * (1000 mm / 1 m) = 5.767 mm
The width of the central maximum on a screen 3.00 m from the slit is approximately 5.767 mm.