To determine the angle that locates the first dark fringe when the width of the slit is 1.20 x 10^-6 m, we can use the formula for the angle of the first dark fringe in a single-slit diffraction experiment.
The formula is given by:
θ = λ / W
where θ is the angle, λ is the wavelength of light, and W is the width of the slit.
Let's plug in the given values:
θ = 680 nm / 1.20 x 10^-6 m
First, we need to convert the wavelength from nanometers (nm) to meters (m).
1 nm = 1 x 10^-9 m
So, 680 nm = 680 x 10^-9 m = 6.8 x 10^-7 m.
Now we can continue with the calculation:
θ = 6.8 x 10^-7 m / 1.20 x 10^-6 m
Dividing the two values, we get:
θ ≈ 0.567
Therefore, the angle that locates the first dark fringe when the width of the slit is 1.20 x 10^-6 m is approximately 0.567 radians.