Help! I have no idea how to solve this:
If the distance between two slits is 0.0550 mm, find the angle between the first-order and second-order bright fringes for yellow light with a wavelength of 605 nm.
To solve this problem, we can use the double-slit interference equation:
λ = (d sin θ) / m
Where:
λ is the wavelength of light
d is the distance between the two slits
θ is the angle between the central maximum and the bright fringe
m is the order of the fringe
First, let's convert the given wavelength of yellow light from nanometers (nm) to meters (m):
605 nm = 605 × 10^(-9) m
Next, let's substitute the given values into the double-slit interference equation:
605 × 10^(-9) m = (0.0550 × 10^(-3) m) sin θ / m
We can rearrange this equation to solve for θ:
sin θ = (605 × 10^(-9) m) / (0.0550 × 10^(-3) m)
sin θ = 0.011000
Now, to find the angle θ, we can take the inverse sine (also known as arcsin) of both sides:
θ = arcsin(0.011000)
Using a calculator, we find that the angle θ is approximately 0.630 degrees.
To find the angle between the first-order and second-order bright fringes, we need to find the difference in angles between the two orders. Since the second-order bright fringe is twice the angle of the first-order bright fringe, we can calculate:
θ_second_order - θ_first_order = 2θ
Substituting the value of θ we found earlier:
θ_second_order - θ_first_order = 2 × 0.630
θ_second_order - θ_first_order = 1.260 degrees
Therefore, the angle between the first-order and second-order bright fringes for yellow light with a wavelength of 605 nm is approximately 1.260 degrees.