White light strikes a diffraction grating (930 lines/mm) at normal incidence. What is the longest wavelength that forms a second-order maximum?
I used the equation [(1/d)sin(90)]/m = wavelength: [(1/0.93m)(1)] /2 = 0.5376m. To convert to nm I multiplied by 10^-9. This is incorrect. Can anyone help? Thanks
Isn't d the reciprocal of 930/mm? or
or 1/d= .001m/930=1.08E-8 m or .108nm?
check my thinking. In your equation, unit wise, if you are to have length on the right, you have to have length units on the left.
I remember the grading equation as
d sinTheta /n= lambda, where d is in meters.
Perhaps that is your error.
The answer should follow such that
Lines/mm --> d --> (1/930mm)/1000mm/m
d = 1.075e-6 meters
set sin theta = 90o = (1)
(dsin(Theta))m=mlambda
(1.075e-6 (1))/2)= 5.375e-7 or 537nm.
To determine the longest wavelength that forms a second-order maximum with a diffraction grating, you need to use the correct equation and a proper understanding of units. Here's how you can approach this:
1. Start with the equation for the diffraction grating:
d * sin(θ) = m * λ
where:
- d is the spacing between the grating lines (given as 930 lines/mm)
- θ is the angle of diffraction (in this case, at normal incidence, it is 90 degrees)
- m is the order of the maximum (in this case, second-order maximum)
- λ is the wavelength of light
2. The spacing between the grating lines (d) given is in mm, but you need to convert it to meters as the equation requires consistent units. The conversion factor from mm to meters is 1/1000. So, d = (1 / 930) mm = (1 / (930 * 1000)) m ≈ 1.0753 × 10^(-6) m.
3. Substituting the known values into the equation:
(1.0753 × 10^(-6) m) * sin(90 degrees) = (2) * λ
The sin(90 degrees) term simplifies to 1, so the equation becomes:
1.0753 × 10^(-6) m = 2 * λ
4. Rearrange the equation to solve for λ:
λ = (1.0753 × 10^(-6) m) / 2
λ ≈ 5.3765 × 10^(-7) m
5. To convert the wavelength to nanometers, multiply by 10^9:
λ ≈ 5.3765 × 10^(-7) m * (10^9 nm/ 1 m)
λ ≈ 537.65 nm
Therefore, the longest wavelength that forms a second-order maximum with this diffraction grating is approximately 537.65 nm.