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 10-6 m

To determine the angle that locates the first dark fringe when the width of the slit is 1.20 * 10^(-6) m, we can use the equation for the angular position of the dark fringes in a single-slit diffraction pattern:

sinθ = mλ / b

Where:
- θ is the angle that locates the fringe,
- m is the order of the fringe (in this case, m = 1 since we are interested in the first dark fringe),
- λ is the wavelength of the light (given as 680 nm or 680 * 10^(-9) m),
- b is the width of the slit (given as 1.20 * 10^(-6) m).

Substituting these values into the equation:

sinθ = (1 * 680 * 10^(-9)) / (1.20 * 10^(-6))

sinθ ≈ 0.5667

To find the angle θ, we can use the inverse sine function (sin^(-1)):

θ = sin^(-1)(0.5667)

Using a calculator or tables, we find that:

θ ≈ 34.5 degrees

Therefore, the angle that locates the first dark fringe when the width of the slit is 1.20 * 10^(-6) m is approximately 34.5 degrees.