In an interference of light experiment, coherent light that contains two wavelengths: 640 nm (red-orange) and 425 nm (indigo-blue), passes through two narrow slits separated by 5.35 μm, and the interference pattern is observed on an observation screen 2.51 m away. (1 μm = 1×10-6 m, 1 nm = 1×10-9 m.)
What is the linear separation on the screen between the third bright fringes produced by the two wavelengths on one side of the central bright fringe in the experiment? (in meters)
Note: There is no need to make a small angle approximation here: you can calculate what you need directly.
Thiiiis question.
Okay, so the only two formulas you need are:
1) dsinθ=mλ
2) y=Ltanθ
You already have all of your variables:
d=5.35x10^-6m
m=3
L=2.51m
λ_blue=4.25x10^-7m
λ_red=6.40x10^-7m
So now, just sub your values into formula 1 to find θ_blue and θ_red, (13.78727427... degrees for blue, and 21.03133713... degrees for red).
From there, just sub your θ_blue and θ_red into formula 2 to find your y_blue and y_red, and then find the difference between the two.
In the end, I think your linear separation should come to something like: 0.3491501095m...I think.
To find the linear separation on the screen between the third bright fringes produced by the two wavelengths on one side of the central bright fringe, we first need to calculate the angular separation between these fringes.
The angular separation between fringes can be given by the formula:
θ = λ / d
where θ is the angular separation, λ is the wavelength of light, and d is the separation between the two slits.
Let's calculate the angular separation for both wavelengths separately:
For the red-orange wavelength (640 nm or 640 × 10^(-9) m):
θ_red-orange = λ_red-orange / d = 640 × 10^(-9) / 5.35 × 10^(-6) rad
For the indigo-blue wavelength (425 nm or 425 × 10^(-9) m):
θ_indigo-blue = λ_indigo-blue / d = 425 × 10^(-9) / 5.35 × 10^(-6) rad
Now, we can find the linear separation on the screen by using the formula:
y = r × L
where y is the linear separation, r is the angular separation, and L is the distance from the slits to the observation screen.
Let L be 2.51 m (given), and let's calculate y for both wavelengths separately:
y_red-orange = θ_red-orange × L = (640 × 10^(-9) / 5.35 × 10^(-6)) × 2.51
y_indigo-blue = θ_indigo-blue × L = (425 × 10^(-9) / 5.35 × 10^(-6)) × 2.51
Finally, the linear separation between the third bright fringes produced by the two wavelengths on one side of the central bright fringe can be calculated by subtracting y_indigo-blue from y_red-orange:
Linear separation = y_red-orange - y_indigo-blue
You can substitute the calculated values into the equation to find the final answer in meters.