When the light of a wavelength 450 nm is passed through a certain diffraction
grating, the first order diffraction maximum is found to be at an angle of 35° to the
straight through. Calculate the distance between adjacent slits in the grating
the difference in path length = 1 wavelength
d sin 35 = 450 *10^-9 meter
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html
To calculate the distance between adjacent slits in the diffraction grating, we can use the equation for the grating equation:
dsinθ = mλ
where d is the distance between adjacent slits, θ is the angle of diffraction, λ is the wavelength of light, and m is the order of the diffraction maximum.
In this case, we are given the wavelength (λ = 450 nm), the angle of diffraction (θ = 35°), and the order of the diffraction maximum (m = 1).
First, we need to convert the angle from degrees to radians:
θ = 35° = 35 * π/180 radians = 0.6109 radians
Next, we can rearrange the grating equation to solve for d:
d = (mλ) / sinθ
Plugging in the values, we get:
d = (1 * 450 nm) / sin(0.6109)
Note: make sure to use radians when taking the sine of the angle.
Calculating the sine of 0.6109 radians:
sin(0.6109) ≈ 0.5694
Now, we can substitute this value back into the equation:
d = (1 * 450 nm) / 0.5694
Simplifying further:
d ≈ 790 nm
Therefore, the distance between adjacent slits in the diffraction grating is approximately 790 nm.