A monochromatic laser beam, with a wavelength of 532 nm passes through a diffraction grating. If the second order diffraction maximum occurs at an angle of 35.0 degrees to the straight through position, calculate the separation of adjacent slits on the grating.
To calculate the separation of adjacent slits on the grating, we can use the formula for angular separation in a diffraction grating:
d * sin(θ) = m * λ
Where:
- d is the separation between adjacent slits on the grating (what we want to find).
- θ is the angle at which the diffraction maximum occurs.
- m is the order of the diffraction maximum.
- λ is the wavelength of the laser beam.
In this case, we have:
- θ = 35.0 degrees (converted to radians, θ = 35.0 * (π/180))
- m = 2 (second order)
- λ = 532 nm (converted to meters, λ = 532 * 10^-9)
Rearranging the formula to solve for d:
d = (m * λ) / sin(θ)
Substituting the given values:
d = (2 * 532 * 10^-9) / sin(35.0 * (π/180))
Calculating the result will give us the separation of adjacent slits on the grating.