Abeam of light passes through a liquid into air. angle 1, angle of
incidence, is 23°. the angle 2, angle of refraction is 38°. refractive
index for air is 1.00. calculate the refractive index of the liquid
medium.

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:  

(1)  

Where:  

is the first medium index of refraction (the value we want to know)

is the second medium index of refraction (air)  

is the angle of incidence

is the angle of refraction

Now, let's find from (1):

(2)  

Substituting the known values:

Finally:

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle