The dependence of the index of refraction on wavelength is called dispersion.A beam of light (in air)containing red and blue light is incident at an angle of 35 $\circ$ on a glass plate that has an index of refraction of 1.64 for blue light and 1.61 for red light.By what percent does the speed of the red light exceed that of the blue light inside the glass,i.e.calculate (v(red)-v(blue))* 100 / v(red)?
A)1.1%
B)1.8%
C)0.53%
D)The speed is the same for both colors.
E)0.019%

Question

Quizplus · Accepted Answer

The speed of light in a medium is given by $v = \frac{c}{n}$, where $c$ is the speed of light in vacuum and $n$ is the index of refraction. For red light, $v_{\text{red}} = \frac{c}{1.61}$ and for blue light, $v_{\text{blue}} = \frac{c}{1.64}$. The percent difference in speed is calculated as $\frac{v_{\text{red}} - v_{\text{blue}}}{v_{\text{red}}} \times 100$. Given that the indices of refraction for red and blue light are 1.61 and 1.64 respectively, the speed of red light is slightly higher than that of blue light due to its lower index of refraction. Calculating the exact percentage gives a result close to 1.8%.

The Dependence of the Index of Refraction on Wavelength Is ∘\circ∘

The Dependence of the Index of Refraction on Wavelength Is $\circ$