Question

The index of refraction for a certain type of glass is 1.643 for blue light and 1.605 for red light. When a beam of white light (one that contains all colors) enters from air a plate of this glass at an incidence angle of 35.05 degree, what is the absolute value of delta, the angle in the glass between blue and red parts of the refracted beams?

Answer 1

The Snell's Law express that:

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

Solving for $\theta _{2}$ for both wavelengths (blue and red) using their refraction index n2, we have:

$\theta _{2Blue}=sin^{-1}(\frac{sin(35,05)}{1,643})=20,459$

$\theta _{2Red}=sin^{-1}(\frac{sin(35,05)}{1,605})=20,966$

Finally, the difference between angles is:

$\left | \theta _{2}-\theta _{1} \right |=\left |20,966- 20,459 \right |=0,507$