A five-slit system with 7.0 um slit spacing is illuminated with 630 nm light. Find the angular positions of the third and sixth minima.
N•d•sinφ = m• λ,
sinφ = m• λ/N•d ,
sinφ3 = 3• 630•10^-9/5•7•10^-6 = 5.4•10^-2, φ3 = 3.095º,
sinφ6 = 6• 630•10^-9/5•7•10^-6 = 10.8•10^-2, φ6 = 6.2º.
To find the angular positions of the third and sixth minima in a five-slit system, we can use the equation for the angular position of the minima in a double-slit interference pattern.
The equation for the angular position of minima in a double-slit interference pattern is given by:
sinθ = m * λ / d
Where:
- θ is the angular position of the minima.
- m is the order of the minima.
- λ is the wavelength of the light.
- d is the slit spacing.
In this case, we have a five-slit system, which means we have five slits and four intervals between them.
To find the angular positions of the third and sixth minima, we need to determine the corresponding values of m. Since we have a five-slit system, the values of m will be multiples of five.
For the third minimum, m = 3 * 5 = 15.
For the sixth minimum, m = 6 * 5 = 30.
Substituting the values into the equation, we get:
sinθ3 = 15 * (630 nm / 1,000 nm) / 7.0 um
sinθ6 = 30 * (630 nm / 1,000 nm) / 7.0 um
To obtain the angular positions, we can take the inverse sine (sin^-1) of both sides of the equations:
θ3 = sin^-1(sinθ3)
θ6 = sin^-1(sinθ6)
Using a scientific calculator or computer software to perform these calculations, you will obtain the values of θ3 and θ6, which are the angular positions of the third and sixth minima, respectively.