Question

A hydrogen discharge lamp emits light with two prominent wavelengths: $656nm$(red) and $486nm$(blue). The light enters

a flint-glass prism perpendicular to one face and then refracts

through the hypotenuse back into the air. The angle between

these two faces is $35°$.

a. Use Figure $35.18$to estimate to $\pm 0.002$the index of refraction

of flint glass at these two wavelengths.

b. What is the angle (in degrees) between the red and blue light

as it leaves the prism?

Short answer

(a) The index of refraction of flint glass at these two wavelengths are$n_R=1.572$and$n_B=1.587$

(b) The angle between the red and blue light as it leaves the prism $1.16°$.

Step-by-step solution

part (a) step 1: Given Information

We need to estimate the index of refraction of flint glass at the two wavelengths.

part (a) step 2: Simply

$$\begin{gathered} \lambda =656nm{n}_R=1.572 \\ \lambda =486nm{n}_B=1.587 \end{gathered}$$.
Here$\lambda$is the wavelength and$n$is refractive index.

part (b) step 1: Given Information

We need to find angle between the red and blue light.

part (b) step 2: Calculation

$$\begin{gathered} n_1\sin {\sigma }_1=n_2\sin {\sigma }_2 \\ {\sigma }_2={\sin }^{-1}\left(\frac{n_1\sin {\sigma }_1}{n_2}\right) \end{gathered}$$

RED: BLUE:

$$\begin{gathered} n_1=1.572n_1=1.587 \\ {n}_2=1.00n_2=1.00 \\ {\sigma }_1=35°{\sigma }_1=35° \\ {\sigma }_2=64.37°{\sigma }_2=65.54° \end{gathered}$$

$\sigma ={\sigma }_B-{\sigma }_R=1.16°$.

Here $n$is the refractive index and$\sigma$refraction angle.

part (b) step 3: Diagram