Answer: 1.57
Explanation:
This described situation is known as Refraction, a phenomenon in which light bends or changes its direction when passing through a medium with a index of refraction different from the other medium.
In this context, the index of refraction is a number that describes how fast light propagates through a medium or material.
According to Snell’s Law:
[tex]n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})[/tex] (1)
Where:
[tex]n_{1}[/tex] is the first medium index of refraction (the value we want to know)
[tex]n_{2}=1[/tex] is the second medium index of refraction (air)
[tex]\theta_{1}=23\°[/tex] is the angle of incidence
[tex]\theta_{2}=38\°[/tex] is the angle of refraction
Now, let's find [tex]n_{1}[/tex] from (1):
[tex]n_{1}=n_{2}\frac{sin \theta_{2}}{sin \theta_{1}}[/tex] (2)
Substituting the known values:
[tex]n_{1}=1\frac{sin(38\°)}{sin(23\°)}[/tex]
Finally:
[tex]n_{1}=1.57[/tex]
