Homework Help: For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of

Re: Confused?

Firstly you gave this equation:

Nmax = 4a/lamda x sqaureroot (N1^2 - N2^2)

Am I correct to think this is equivalent?

[itex] N_{max}=\frac{4a}{λ} \sqrt{n_{1}^{2}-n_{2}^{2}} [/itex]

(I would suggest in future as opposed to using "x" to indicate multiplies, I would use "*". Simply for clarity)

If this is the case begin by squaring both sides of the equation, and then attempt to isolate the [itex] n_{2} [/itex] term.

 

Re: Confused?

Find an equation for n2, and then try to understand what this means.

 

Re: Confused?

This is due to you doing it on a calculator. Rearrange it on paper, so that you have

n2= ...

 

Re: Confused?

The term [itex] \sqrt{n_{1}^{2}-n_{2}^{2}}=\sqrt{(n_{1}^{2}-n_{2}^{2})} [/itex]

So by squaring you will get

[itex] N_{max}^{2}=(\frac{4a}{λ})^{2} (n_{1}^{2}-n_{2}^{2}) [/itex]

It would be more convenient if you multiplied both sides of [itex] (\frac{λ}{4a})^{2} [/itex] rather than multiplying out the brackets.