A screen $1\mathrm{.}0mm$ behind a diffraction grating shows $5$ bright spots. The first set of interference

fringes is $43\mathrm{.}6cm$ from the center point and the second set is an additional $89\mathrm{.}7cm$ from the

first set of fringes. The wavelength of light is $600nm.$ How many lines per millimeter does the

grating have?

A$.$ Understand the problem $-$ list the relevant quantities. For each quantity list a name,

symbol, units, and either the given number or mark as unknown.

B$.$ Identify assumptions $-$ write what you are assuming$/$idealizing about the diffraction

grating and the light passing through it$.$ Include here what model of light you're using and

why it is applicable.

C$.$ Represent the situation physically $-$ draw and label a diagram of the situation. An

appropriate diagram should always be a professional representation that includes

specific details helpful to the situation $($not just a simple picture!$).$ Include detailed labels

for all crucial quantities related to or listed in part $A.$

D$.$ Represent principles symbolically $-$ Write the name of any equations you'll use and

write the equation. If there are conditions for this equation being used, explain how these

are met. Be sure to indicate how the variables in the equation relate to what you listed in

Part $A($use the same letters or give a legend$)$

E$.$ Find unknown$($s$)$ symbolically $-$ without numbers, find any unknown$($s$)$ in terms of

symbols representing known quantities.

F$.$ Plug in numbers $-$ plug numbers $($with units$)$ into your symbolic answer!

G$.$ Are the units correct? State the units you expect the unknown quantity to have. Show

that the algebraic expression of your final answer reduces $($cancels out$)$ to have those

same units.

H$.$ Is your numerical answer reasonable for the problem? Did you expect your final

answer to be a scalar or a vector? Is that what you got? Relate this to the diffraction

glasses you played with in class. Is your answer in the same ballpark as the range of

those glasses? Be sure to explain how you conclude that.

I. Does the physics of your symbolic answer match the real world physics? Analyze

your symbolic solution. Use your real$-$world intuition to decide if number of lines per

millimeter would increase$/$decrease if the distance from the central maximum to the next

interference fringe would increase? Does your symbolic solution match this conclusion?

$($you may need to do some math to help you conclude this$)$ Be sure to explain your

reasoning.