Laser light with a wavelength = 665 illuminates a pair of slits at normal incidence.
What slit separation will produce first-order maxima (i.e. m=1) at angles of 8 from the incident (or straight through) direction? Remember, 1 nm = m.
Express your answer using two significant figures, in micrometres ().
all I know is that it's not simply
n(wavelength)=dsin(theta) because I plugged the numbers in and they were wrong. (n=1)
To find the slit separation that produces the first-order maxima, we can use the equation for the position of maxima in a double-slit interference pattern:
sinθ = mλ / d
where:
θ is the angle of the maxima (8° in this case),
m is the order of the maxima (1 for first-order),
λ is the wavelength of light (665 nm),
and d is the slit separation that we need to find.
Rearranging the equation to solve for d:
d = mλ / sinθ
Now we can plug in the values and calculate the slit separation:
d = (1 * 665 nm) / sin(8°)
Remember to convert nm to µm by dividing by 1000:
d = (1 * 0.665 µm) / sin(8°)
Using a calculator:
d ≈ 4.9 µm
Therefore, the slit separation that will produce first-order maxima at an angle of 8° is approximately 4.9 µm.