Question

A Michelson interferometer had a mirror velocity of $2.75\mathrm{cm}/\mathrm{s}$. What would be the frequency of the interferogram for

(a) UV radiation of $350\mathrm{nm}$

(b) visible radiation of $575\mathrm{nm}$

(c) IR radiation of $5.5\mathrm{\mu m}$

(d) IR radiation of $25\mathrm{\mu m}$

Short answer

$$\begin{gathered} \mathrm{a})1.6\times {10}^5\mathrm{Hz} \\ \mathrm{b})9.6\times {10}^4\mathrm{Hz} \\ \mathrm{c})1\times {10}^4\mathrm{Hz} \\ \mathrm{d})2.2\times {10}^3\mathrm{Hz} \end{gathered}$$

Step-by-step solution

Given information

$$\begin{gathered} v_m=2.75\mathrm{cm}/\mathrm{s} \\ a)𝜆=350\mathrm{nm} \\ b)𝜆=575\mathrm{nm} \\ c)𝜆=5.5\mathrm{\mu m} \\ d)𝜆=25\mathrm{\mu m} \end{gathered}$$

Formula

$F=\frac{2v_m}{𝜆}$

Wher

$$\begin{gathered} F=Frequency \\ {v}_m=velocity \\ 𝜆=wavelength \end{gathered}$$

Part a) Step 1: Calculation

Putting values in formula

$$\begin{gathered} F=\frac{2\times 2.75\times {10}^{-2}}{350\times {10}^{-9}} \\ F=1.6\times {10}^5\mathrm{Hz} \end{gathered}$$

Part b) Step 1: Calculation

Putting values in formula

$$\begin{gathered} F=\frac{2\times 2.75\times {10}^{-2}}{575\times {10}^{-9}} \\ F=9.6\times {10}^5\mathrm{Hz} \end{gathered}$$

Part c) Step 1: Calculation

Putting values in formula

$$\begin{gathered} F=\frac{2\times 2.75\times {10}^{-2}}{5.5\times {10}^{-6}} \\ F=1\times {10}^4\mathrm{Hz} \end{gathered}$$

Part d) Step 1: Calculation

Putting values in formula

$$\begin{gathered} F=\frac{2\times 2.75\times {10}^{-2}}{25\times {10}^{-6}} \\ F=2.2\times {10}^3\mathrm{Hz} \end{gathered}$$