Mode Structure of Helium$-$Neon Laser

The mode structure of a HeNe$-$laser of wavelength $633nm$ is studied with a scanning Fabry$-$Perrot interferometer. The two laser concave mirrors have the same radius of curvature. On an oscilloscope the following image is obtained.

$1-$ Calculate the frequency difference between $TE{M}_{00q}$ and $TE{M}_{00q+1}.$

$2-$ Calculate the cavity length of the Fabry$-$Perrot interferometer and the laser.

$3-$ Name the peaks $A,C,D,F,$ if the peak $B$ is the $TE{M}_{01q}.$

$4-$ Draw a picture of how the image would look like on the oscilloscope if the laser was of type single mode frequency.

$5-$ Calculate the curvature of the two laser mirrors based on your discussion in questions $2$ and $3.$

$6-$ Name the peaks $D$ and $E.$

$7-$ What is the Rayleigh distance $z_0?$

$8-$ Calculate the "Gouy" Phase shift.

You may find th

$1$

A $250,000$ BPCD of crude oil has the TBP distillation data presented as volume percent distilled versus distillation temperature, $C.$

$\backslash$table$[[$Vol$.\%,0,10,30,50,70,90],[$TBP$,C,35,160,250,260,390,505]]$

The average boiling point of the crude oil is $290C$ and the API density is $28$ degrees with a characterization factor, $K$ equal to $11\mathrm{.}33.$ Plot data on an Excel sheet. $(2$ mark$)$

a$)$ Calculate the critical temperature, the critical pressure, and the eccentric factor. Using Excel spreadsheet. $(1\mathrm{.}5$ marks$)$

b$)$ Calculate the enthalpy of this crude oil $($or furnace load$)$ using the Lee$-$Kessler correlation with a reference state of ideal gas $298K$ if the crude is heated from $150$ to $366C.$ Note: Use equations $3\mathrm{.}38$ to $3\mathrm{.}41$ of your textbook if needed in calculations. Use Excel. $(5$ marks$)$

c$)$ If this crude oil is fed to a distillation column, how much Naphtha and kerosine are produced BPCD if the EP of naphtha is $120C$ and the IBP of Diesel is $248C?1\mathrm{.}5$ marks$).$