Particular glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and 1.615 for red light of wavelength 680 nm.Consider a beam containing these two colors incident on this piece of glass,at an angle of 30 degrees from the normal.What is the angle between the red and the blue beam in the glass?

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Quizplus · Accepted Answer

The angle between the red and blue beams in the glass can be found using Snell's law, which states $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the indices of refraction of the first and second mediums, respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively. Given the indices of refraction for blue (1.650) and red (1.615) light and the angle of incidence (30 degrees), we can calculate the angles of refraction for both colors. The difference in these angles will give the angle between the red and blue beams in the glass.For blue light:$$1.000 \sin(30^\circ) = 1.650 \sin(\theta_{\text{blue}})$$$\sin(\theta_{\text{blue}}) = \frac{\sin(30^\circ)}{1.650}$For red light:$$1.000 \sin(30^\circ) = 1.615 \sin(\theta_{\text{red}})$$$\sin(\theta_{\text{red}}) = \frac{\sin(30^\circ)}{1.615}$After calculating $\theta_{\text{blue}}$ and $\theta_{\text{red}}$, the difference in angles ($\theta_{\text{blue}} - \theta_{\text{red}}$) gives the angle between the red and blue beams in the glass. This calculation results in a small angle difference, which is closest to 0.4 degrees, indicating that the beams are slightly diverged inside the glass due to the difference in refraction angles caused by their different wavelengths and corresponding indices of refraction.

Particular Glass Has an Index of Refraction of 1