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

Step-by-step explanation:

We know, Snell's law,

`n_1sini=n_2sinr`

For, the red light,

`\begin{gathered} 1* sin42\degree=1.515sinr_r \\ sinr_r=(sin42\degree)/(1.515) \\ r_r=sin^(-1)(0.4417) \\ r_r=26.2\degree \end{gathered}`

For, the blue light,

`\begin{gathered} 1* sin42\degree=1.523sinr_b \\ r_b=sin^(-1)(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.