Question

The index of refraction for a certain type of glass is 1.641 for blue light and 1.603 for red light. When a beam of white light (one that contains all colors) enters a plate of glass from the air at an incidence angle of 40.05∘, what is the absolute value of ????, the angle in the glass between blue and red parts of the refracted beams?

Answer 1

Answer:

The angle between the emergent blue and red light is $0.566^{o}$

Explanation:

We have according to Snell's law

$n_{1}sin(\theta _{i})=n_{2}sin(\theta _{r})$

Since medium from which light enter's is air thus $n_{1}=1$

Thus for blue incident light we have

$1\times sin(40.05)=1.641\times sin(\theta _{rb})\\\\\therefore \theta _{rb}=sin^{-1}(\frac{sin(40.05)}{1.64})\\\\\theta _{rb}=23.10$

Similarly using the same procedure for red light we have

$1\times sin(40.05)=1.603\times sin(\theta _{rr})\\\\\therefore \theta _{rr}=sin^{-1}(\frac{sin(40.05)}{1.603})\\\\\theta _{rr}=23.66^{o}$

Thus the absolute value of angle between the refracted blue and red light is

$|23.66-23.10|=0.566^{o}$