2
$\begingroup$

Last year, our teacher made us an exam to check our knowledge in light reflection and refraction. I don't perfectly remember it, but I know that one of the exercises included a ray with its angle of incidence, and let's say 7 media with their respective indexes of refraction. We had to find the last angle of refraction. Even though it's fairly easy to do, it took my classmates a lot of time. Meanwhile I didn't even have time to reach that question: we were very limited on time.

I was thinking if there was another way to find it, a quicker one. Then, while looking at a figure of refraction in my physics book, I came up with an idea: what if we calculate it using only $n_1$, $n_7$, $\Theta_1$ and $\Theta_7$? I'll explain.

Let's say the first medium is air, and I'm calling it $n_1$. The seventh medium is glass, and I'm calling it $n_7$. There are 5 other media between air and glass. The angle of incidence will be $\Theta_1$ and the last angle of refraction, the one inside $n_7$, will be $\Theta_7$. Is it possible to calculate $\Theta_7$ as

$$\Theta_7 = \frac{n_7 \cdot \Theta_1}{n_1},$$

or is it required to calculate each angle of refraction one by one until we reach $\Theta_7$?

$\endgroup$
1
  • $\begingroup$ That should work. You're going to lose a bunch of light to reflection along the way though... $\endgroup$
    – M. Enns
    Apr 21 '19 at 16:48
2
$\begingroup$

Yes, you are right, except for that it is not the division of $\theta$, but $\sin\theta$. However, the real reason what you said is true can be seen by a bit of observation.

$$n_i\sin(\theta_i) = constant$$

Because:

$$\frac{n_2}{n_1} = \frac{\sin\theta_1}{\sin\theta_2}$$

And for the ray going to the third medium from the second,

$$\frac{n_3}{n_2}=\frac{\sin\theta_2}{\sin\theta_3}$$

What do you see in common (try rearraging them)?

$$n_1\sin\theta_1=n_2\sin\theta_2=n_3\sin\theta_3 ...$$

$\endgroup$
1
  • 1
    $\begingroup$ Yesss I forgot the sinuses! That's why I'm bad at physics 😅. Thankss now it totally makes sense!! $\endgroup$
    – Arbri Ibra
    Apr 21 '19 at 16:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.