In an experiment conducted by Young using sodium light with λ=589 nm, the slits are 1 μm wide. You notice that every fourth fringes missing.
a) What is the slit separation?
d = na = 4(1 μm) = 4 μm.
b) How many fringes appear on the screen?
I'm not sure how to do this part.
so for part b:
d*sin(theta)=m*λ
when you plug in the d from part a and λ and 90 degree for theta(maximum theta). you get m=6.8. This is for one side of the slit. You must subtract the missing fringes, 4 th one. you get m=5. m=10 for both side of the screen and add one for the center fringe you get m=11.
To determine the number of fringes that appear on the screen, you can use the formula for the fringe width in Young's double-slit experiment:
wavelength (λ) = fringe width (w) * distance to screen (L) / distance between slits (d)
Since we know the values of λ, w, and d, we can rearrange the formula to solve for the number of fringes (N):
N = L * λ / (w * d)
However, in this case, we want to find the number of fringes missing, so we can subtract the missing fringes from the total number of fringes:
N_missing = N_total - N_visible
To calculate the total number of fringes, we need to know the maximum number of fringes that can be seen. This can be determined by finding the maximum fringe position (θ_max) using the following formula:
θ_max = λ / d
Then, we can calculate the total number of fringes using the angular position (θ) of the missing fringes:
N_total = θ / θ_max
Substituting these values into the equation, we can find the missing fringes:
N_missing = N_total - N_visible
Remember to convert all values to the appropriate units (e.g., radians for angular position) before performing calculations.