Question

1. The function of lenses is based on the law of refraction. A light beam is traveling from the medium 1 where its speed is V1, to the medium 2 where its speed is V2 = 0.8 V1. a) If the first medium is the air (n1 = 1), what is the index of refraction for the second medium?

Answer 1

Answer:

The index of refraction for Medium 2 would be 1.25

Step-by-step explanation:

We have the following data:

Speed of light in Medium 1 = V₁

Speed of light in Medium 2 = V₂

The speed of Light in Medium 2 is related to speed of light in Medium 1 as:

V₂ = 0.8 V₁

Moreover, it is given that Medium 1 is air with index of refraction equal to 1. i.e.

n₁ = 1

We need to find the index of refraction for medium 2. Lets name it is as n₂.

Snell's law related the above mentioned 4 quantities by following relation:

The ratio of indices of refraction of 2 mediums is equivalent to the reciprocal of ratio of  phase velocities in those 2 mediums. Mathematically, this can be written as:

$\frac{n_{1}}{n_{2}} = \frac{V_{2}}{V_{1}}$

Substituting the values we have gives us:

$\frac{1}{n_{2}}=\frac{0.8V_{1}}{V_{1}} \\\\\frac{1}{n_{2}}=0.8\\\\ 1=0.8n_{2}\\\\\frac{1}{0.8}=n_{2}\\\\ n_{2}=1.25$

This means, the index of refraction for Medium 2 would be 1.25