## anonymous one year ago What is the critical angle theta c for total internal reflection if the material is clear acrylic, with a refractive index of 1.5? 62 degrees, 90 degrees , 42 degrees , or 49 degrees :/

1. Michele_Laino

here we have to apply the law of Snell, so we can write this: $n\sin {\theta _c} = 1$

2. Michele_Laino

then: $\large \sin {\theta _c} = \frac{1}{n} = \frac{1}{{1.5}}$

3. anonymous

so we get 0.666666667?

4. Michele_Laino

ok! Now we have to compute this: ${\theta _c} = \arcsin \left( {0.667} \right) = ...$

5. Michele_Laino

$\large {\theta _c} = \arcsin \left( {0.667} \right) = ...$

6. anonymous

41.835? so our solution is 42 degrees?

7. Michele_Laino

yes!

8. anonymous

yay! thank you:)

9. Michele_Laino

:)