Question

The index of refraction of crown glass is 1.515 for red light and 1.523 for blue light. Find the angle separating rays of the two colors in a piece of crown glass if their angle of incidence is 42o .

Answer 1

Given:

The angle of incidence is,

$i=42\degree$

The refractive index of the crown glass for red light is,

$n_r=1.515$

The refractive index of the crown glass for blue light is,

$n_b=1.523$

To find:

The angle separating rays of the two colours in a piece of crown glass

Explanation:

We know, Snell's law,

$n_1sini=n_2sinr$

For, the red light,

$\begin{gathered} 1\times sin42\degree=1.515sinr_r \\ sinr_r=\frac{sin42\degree}{1.515} \\ r_r=sin^{-1}(0.4417) \\ r_r=26.2\degree \end{gathered}$

For, the blue light,

$\begin{gathered} 1\times sin42\degree=1.523sinr_b \\ r_b=sin^{-1}\frac{sin42\degree}{1.523} \\ r_b=26.1\degree \end{gathered}$

The separation between the refracted rays is,

$\begin{gathered} r_r-r_b=26.2\degree-26.1\degree \\ =0.1\degree \end{gathered}$

Hence, the required separation is 0.1 degrees.