Can I see the answer? You just wasted points, but thank youuu
For the total internal reflection of a substance, we can express the relationship between the critical angle,
![\theta_{c}](https://tex.z-dn.net/?f=%20%5Ctheta_%7Bc%7D%20)
, and the indices of refraction as
(1) <span>
</span>
where
![n_{1}](https://tex.z-dn.net/?f=n_%7B1%7D)
and
![n_{2}](https://tex.z-dn.net/?f=n_%7B2%7D)
are the indices of refraction. And under polarization, we can express Snell's Law as
![n_{1} sin(\theta_{p}) = n_{2}sin(90-\theta_{p})](https://tex.z-dn.net/?f=n_%7B1%7D%20sin%28%5Ctheta_%7Bp%7D%29%20%3D%20n_%7B2%7Dsin%2890-%5Ctheta_%7Bp%7D%29%20)
Rearranging this we have
![n_{1} sin(\theta_{p}) = n_{2}cos(\theta_{p})](https://tex.z-dn.net/?f=n_%7B1%7D%20sin%28%5Ctheta_%7Bp%7D%29%20%3D%20n_%7B2%7Dcos%28%5Ctheta_%7Bp%7D%29)
![\frac{sin(\theta_{p}}{cos(\theta_{p})} = \frac{n_{2}}{n_{1}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28%5Ctheta_%7Bp%7D%7D%7Bcos%28%5Ctheta_%7Bp%7D%29%7D%20%3D%20%5Cfrac%7Bn_%7B2%7D%7D%7Bn_%7B1%7D%7D%20)
(2)Substituting equations (1) into (2), we have
![tan(\theta_{p}) = \frac{n_{1} sin(\theta_{c})}{n_{1}}](https://tex.z-dn.net/?f=%20tan%28%5Ctheta_%7Bp%7D%29%20%3D%20%5Cfrac%7Bn_%7B1%7D%20sin%28%5Ctheta_%7Bc%7D%29%7D%7Bn_%7B1%7D%7D%20)
![tan(\theta_{p}) = sin(\theta_{c})](https://tex.z-dn.net/?f=%20tan%28%5Ctheta_%7Bp%7D%29%20%3D%20sin%28%5Ctheta_%7Bc%7D%29%20)
Substituting the value of the critical angle, we have
![tan(\theta_{p}) = sin(42)](https://tex.z-dn.net/?f=%20tan%28%5Ctheta_%7Bp%7D%29%20%3D%20sin%2842%29%20)
Answer: 33.79°
20,000 because I did the quiz and got it right txt me if you need help
Answer:
yes i think that inner planets should be explored because if we ever find new life or are able to live there then i think its worth takeing a risk.
Explanation: