CD Diffraction

In this lab we began by shining a laser on the CD and looking at the diffraction of the laser onto another surface. The observed points would give us the first maxima of the laser. We then measured the distance we could determine the diffraction grating of the CD. The wavelength of the laser was already known for this lab.

The laser on the CD

The diffraction of the laser from the CD

We can find the diffraction grating with this formula dsin(θ) = mλ, in this formula d represents the diffraction grating. We can rearrange this equation for d and the result is, d = mλ/sin(θ). Sin(θ) is the distance measured from the maxima. m is an integer value based on how many maximas have been measured. λ is the wavelength of the laser. L and x are the sides of the triangle used for sin(θ).Arctan(x/L) can be used to find the value of θ

L = 68.5 cm + 0.2 cm

x = 28.8 cm + 0.2 cm

The wavelength of the laser was  λ  = 632.8 nm. 

The value of θ = 22.80° + 0.00269°

m = 1 because we measured the distance to the first maxima. 

When plugging these values into the formula we can determine that d = 1.633 * 10^-6m = 1633nm + 1.8735 * 10^-6 nm

The actual value of the CD's diffraction grating is 1600 nm. The percent error for this lab is 2.1%. The error from this lab is low compared to the usual value of 5%. 

The uncertainty for the values of L and x came from our inaccuracy in the measuring tools. 

The error for terms that were not measured during the lab were determined by using partial derivatives.

There is no error for λ because the laser mas made with extreme accuracy and precision. 

The error for θ can be found by:

 Δθ = sqrt((∂θ/∂x)^2*Δx^2 + (∂θ/∂L)^2*ΔL^2) = 0.00269

The error for d can be found by:

Δd = sqrt((∂d/∂θ)^2*Δθ^2+(∂d/∂λ)^2*Δλ^2), Δλ is zero because there is no error and the error reduces to: d = sqrt((∂d/∂θ)^2*Δθ^2) = 1.8735*10*-15 m