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
b•sinψ = k•λ.
sinψ = k•λ/b = 1•680•10^-9/1.2•10^-6 =
= 0.567
ψ = 34.52 degr
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.