# Change of angle if refractive index changes for 10^-6

• AncientOne99

#### AncientOne99

Homework Statement
The following expression sin ϑ = 1 / n applies to the angle of total reflection at the transition of the beam from glass to air. For how much
changes the angle if the refractive index changes by 10^−6?
For n take 1.5. Express the result only with n.
Relevant Equations
sin(ϑ) = 1/n(water)
Solution:
(delta (ϑ)) =
-(minus delta n) /(n*sqrt((n^2-1)))

Yes i know the solution, but i don't know the steps.

Do you know how to take differentials? For example
##d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.##

Apply this idea to find ##d(\sin\theta)## and ##d(\frac{1}{n})## and set them equal.

kuruman said:
Do you know how to take differentials? For example
##d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.##

Apply this idea to find ##d(\sin\theta)## and ##d(\frac{1}{n})## and set them equal.
Yes, i know how to take the diferentials, but there is no equation to diferentiate or i don't know it.

I solved it, thanks for your help !

kuruman