Answer :
(1) sin 40° = n(sin 200⁰).
1. A ray of light traveling from air into crown glass strikes the surface at an angle of 30°.
We can often use Snell's Law to help us find the index of refraction of a refractive medium.
Snell's Law: [tex]\dfrac{n_1}{n_2}=\dfrac{\sin(\theta_2)}{\sin(\theta_1)}[/tex]
- [tex]n_1[/tex] = the refractive index of the first medium
- [tex]n_2[/tex] = the refractive index of the second medium
- [tex]\theta_1[/tex] = the angle of incidence
- [tex]\theta_2[/tex] = the angle of refraction
In this question, we're given the following:
- The angle of incidence is [tex]40^\circ[/tex] ⇒ [tex]\theta_1=40^\circ[/tex]
- The first medium is air, which has a refractive index of 1.0003 ⇒[tex]n_1 = 1.0003[/tex]
- The angle of refraction is [tex]29^\circ[/tex] ⇒ [tex]\theta_2=29^\circ[/tex]
- Solve for [tex]n_2[/tex].
Since we know we're solving for the index of refraction of the second medium, isolate [tex]n_2[/tex] in Snell's Law:
[tex]\dfrac{n_1}{n_2}=\dfrac{\sin(\theta_2)}{\sin(\theta_1)}\\\\\\\dfrac{n_2}{n_1}=\dfrac{\sin(\theta_1)}{\sin(\theta_2)}\\\\\\n_2=\dfrac{\sin(\theta_1)}{\sin(\theta_2)}*n_1[/tex]
Plug in all the information we know and find [tex]n_2[/tex]:
[tex]n_2=\dfrac{\sin(40^\circ)}{\sin(29^\circ)}*1.0003\\\\\\n_2\approx1.3263[/tex]
Answer
Therefore, the index of refraction of the refractive medium is approximately 1.3263.