A diffraction pattern forms when light passes through a single slit. The wavelength of the light is 680 nm. Determine the angle that locates the first dark fringe when the width of the slit is each of the following.
(b) 1.20 x 10^-6 m
To determine the angle that locates the first dark fringe in a single-slit diffraction pattern, we can use the equation:
sin(θ) = m * λ / w
Where:
θ = angle
m = order of the dark fringe
λ = wavelength of light
w = width of the slit
In this case, we are looking for the first dark fringe, so m = 1. The wavelength of light is given as 680 nm, which we need to convert to meters (since the width of the slit is given in meters). Therefore,
λ = 680 nm = 680 x 10^(-9) m
The width of the slit is given as 1.20 x 10^(-6) m. Substituting these values into the equation,
sin(θ) = (1 * 680 x 10^(-9) m) / (1.20 x 10^(-6) m)
Now, we can calculate the value inside the brackets:
(1 * 680 x 10^(-9) m) / (1.20 x 10^(-6) m) = 0.5667
Next, we need to find the inverse sine (sin^(-1)) of this value:
θ = sin^(-1)(0.5667)
Using a calculator, we find that sin^(-1)(0.5667) ≈ 35.48°
Therefore, the angle that locates the first dark fringe when the width of the slit is 1.20 x 10^(-6) m is approximately 35.48°.