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

For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of the incident light, from medium 1 to medium 2 is reflected?

Im using Sin ic = n1/n2

For Sin ic i get =1.706

But the reverse Sin of that comes up math error?

HELP

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Doc Al
Mentor

Im using Sin ic = n1/n2
You're mixing up n1 and n2. Start from Snell's law and derive the expression for total internal reflection.

Thank you!

I need help rearranging the equation too, im finding it impossible!

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

I need to find n2

Firstly you gave this equation:

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

Am I correct to think this is equivalent?

$N_{max}=\frac{4a}{λ} \sqrt{n_{1}^{2}-n_{2}^{2}}$

(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 $n_{2}$ term.

I have no idea how to rearrange this.

i know by squaring both sides the sqaure root will disappear. But on the other side Nmax = 1.

How does it rearrange so i get a positive number to square root to find n2?

Doc Al
Mentor

i know by squaring both sides the sqaure root will disappear. But on the other side Nmax = 1.
So?
How does it rearrange so i get a positive number to square root to find n2?
Start by squaring both sides and then go from there.

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

Im so confused :(

every time i try to rearrange to find n2 i get math error!

Doc Al
Mentor

every time i try to rearrange to find n2 i get math error!
Show what you did symbolically, step by step.

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

n2= ...

Do I have to multiply out the brackets?

The term $\sqrt{n_{1}^{2}-n_{2}^{2}}=\sqrt{(n_{1}^{2}-n_{2}^{2})}$

So by squaring you will get

$N_{max}^{2}=(\frac{4a}{λ})^{2} (n_{1}^{2}-n_{2}^{2})$

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