a light ray of wave length 589 nm is incident on glass with an angle of incidence of 30. the index of refrection of glass is 1.52 1) what is tye angle of refrection. 2) what are the speed and wavelength of light inside tye glass
Answers
Explanation:
Question: A light-ray of wavelength $\lambda_1 = 589$nm traveling through air is incident on a smooth, flat slab of crown glass (refractive index 1.52) at an angle of $\theta_1=
30.0^\circ$ to the normal. What is the angle of refraction? What is the wavelength $\lambda_2$ of the light inside the glass? What is the frequency $f$ of the light inside the glass?
Answer: Snell's law can be written
\begin{displaymath}
\sin\theta_2 = \frac{n_1}{n_2} \,\sin\theta_1.
\end{displaymath}
In this case, $\theta_1=30^\circ$, $n_1\simeq 1.00$ (here, we neglect the slight deviation of the refractive index of air from that of a vacuum), and $n_2= 1.52$. Thus,
\begin{displaymath}
\sin\theta_2 =\frac{(1.00)}{(1.52)}\,(0.5)=0.329,
\end{displaymath}
giving
\begin{displaymath}
\theta_2 = 19.2^\circ
\end{displaymath}
as the angle of refraction (measured with respect to the normal).
The wavelength $\lambda_2$ of the light inside the glass is given by
\begin{displaymath}
\lambda_2 = \frac{n_1}{n_2}\,\lambda_1 = \frac{(1.00)}{(1.52)}\,(589)
= 387.5\,{\rm nm}.
\end{displaymath}
The frequency $f$ of the light inside the glass is exactly the same as the frequency outside the glass, and is given by
\begin{displaymath}
f = \frac{c}{n_1\,\lambda_1} = \frac{(3\times 10^8)}{(1.00)\,(589\times 10^{-9})}
=5.09\times 10^{14} \,{\rm Hz}.
\end{displaymath}