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

Sloan650
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

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.

Sloan650

Thank you!

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

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

I need to find n2

gash789

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.

Sloan650

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?

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.

gash789

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

Sloan650

Im so confused :(

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

Mentor

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

gash789

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

n2= ...

Sloan650
Do I have to multiply out the brackets?

gash789

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.