Final answer:
The angle of the first minimum for 550-nm light falling on a single slit of width 1.00 μm is 10.0º. There will not be a second minimum.
Step-by-step explanation:
To find the angle of the first minimum for 550-nm light falling on a single slit of width 1.00 μm, we can use the formula:
sin(θ) = mλ/w
where θ is the angle of the first minimum, m is the order of the minimum (in this case, m = 1), λ is the wavelength of the light, and w is the width of the slit.
Plugging in the values, we get:
sin(θ) = (1)(550 × 10-9 m)/(1.00 × 10-6 m)
Taking the inverse sine of both sides, we find:
θ = sin-1((1)(550 × 10-9))/(1.00 × 10-6)
Solving this equation will give us the angle of the first minimum. In this case, the correct answer is (a) 10.0º for the angle of the first minimum.
As for the second minimum, we can use the formula:
sin(θ') = (m+1)λ/w
where θ' is the angle of the second minimum. Plugging in the values, we get:
sin(θ) = (2)(550 × 10-9 m)/(1.00 × 10-6 m)
Taking the inverse sine of both sides, we find:
θ' = sin-1((2)(550 × 10-9))/(1.00 × 10-6)
If we solve for the angle of the second minimum, we find that the correct answer is (b) No, there will not be a second minimum.