Question

The index of refraction of silicate flint glass for red light is 1.620 and for violet light is 1.660 . A beam of white light in this glass strikes the glass–air interface at a 23.90° angle of incidence and refracts out into the air. What is the angular separation between the red and violet components of the spectrum that emerges from the glass?

Answer 1

Answer:

The angular separation equals $0.35^{o}$

Explanation:

We have according to Snell's law

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

$\therefore \theta _{2}=sin^{-1}(\frac{n_{1}sin(\theta _{1})}{n_{2}})$

Using this equation for both the colors separately we have

$\theta _{red}=sin^{-1}(\frac{sin(23.90^{o})}{1.62})\\\\\theta _{red}=14.48^{o}$

Similarly for violet light we have

$\theta _{violet}=sin^{-1}(\frac{sin(23.90^{o})}{1.660})\\\\\theta _{violet}=14.13^{o}$

Thus the angular separation becomes

$\Delta \theta =14.48-14.13=0.35^{o}$