Question

Help please!

A ray of light is incident upon a strange material at an angle of 27 deg from the normal.
Its angle of refraction in the material is 11 deg.
Based on the table below, how would we identify this material?
Clue: the index of refraction in air is 1

A) diamond

B) glass, flint

C) plexiglass

D) zircon

Answer 1

Answer: Diamond

Explanation:

This described situation is known as Refraction, a phenomenon in which the light bends or changes it 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:  

$n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})$ (1)  

Where:  

$n_{1}=1$ is the first medium index of refraction  (air)

$n_{2}$ is the second medium index of refraction (the value we want to know)

$\theta_{1}=27\°$ is the angle of the incident ray  

$\theta_{2}=11\°$ is the angle of the refracted ray

Now, let's find $n_{2}$ from (1):

$n_{2}=n_{1}\frac{sin(\theta_{1}}{sin(\theta_{2}}$ (2)  

Substituting the known values:

$n_{2}=(1)\frac{sin(27\°)}{sin(11\°)}}$

Finally:

$n_{2}=2.379\approx 2.4$

If we compare this result with the given table, the index of refraction value that is close to this number is diamond's index of refraction.

Therefore, the correct option is A: the material is diamond.