Law of Reflection, Snell's Law of Refraction, Total Internal Reflection
On an optical disc with a semicircular lens, we demonstrate the law of reflection, Snell's law of refraction, and the phenomenon of total internal reflection.
The law of reflection states that the angle of incidence is equal to the angle of reflection (angles are always measured as deviations from the normal to the interface).
Snell's law of refraction relates the angles of incidence $\vartheta_1$ and transmission $\vartheta_2$ as $n_1 \sin \vartheta_1 = n_2 \vartheta_2$, where $n_1$ and $n_2$ are the refractive indices of the respective media. For $n_1 < n_2$ – that is, transmission from an optically less dense to an optically denser medium – $\vartheta_1 > \vartheta_2$ – so-called refraction toward the normal occurs. For $n_1 > n_2$ – transmission from an optically denser to an optically less dense medium – $\vartheta_1 < \vartheta_2$ – so-called refraction away from the normal occurs.
However, the angle of transmission cannot be greater than 90°. For transmission from an optically denser to an optically less dense medium, there exists a critical angle of incidence $\vartheta_1 = \vartheta_C$, when $\vartheta_2 = \frac{\pi}{2}$. From Snell's law it follows immediately that $\sin \vartheta_C = \frac{n_2}{n_1}$. For angles of incidence greater than the critical angle, light does not pass through and total internal reflection occurs.
Apparatus. Adjustable lamp, lens f = +150 mm with attached slits, optical disc with semicircular lens.
Detail of slits attached to the lens.
Refraction from an optically less dense to an optically denser medium. Angle of incidence 0°.
Refraction from an optically less dense to an optically denser medium. Angle of incidence 30°. The beam bends toward the normal.
Refraction from an optically less dense to an optically denser medium. Angle of incidence 45°. The beam bends toward the normal.
Refraction from an optically less dense to an optically denser medium. Angle of incidence 60°. The beam bends toward the normal.
Refraction from an optically less dense to an optically denser medium. Angle of incidence 80°. The beam bends toward the normal.
Refraction from an optically less dense to an optically denser medium. Angle of incidence nearly 90°. The beam bends toward the normal.
Refraction from an optically denser to an optically less dense medium. Angle of incidence 0°.
Refraction from an optically denser to an optically less dense medium. Angle of incidence 15°. The beam bends away from the normal.
Refraction from an optically denser to an optically less dense medium. Angle of incidence 30°. The beam bends away from the normal.
Refraction from an optically denser to an optically less dense medium. Angle of incidence 40°. The beam bends away from the normal.
Refraction from an optically denser to an optically less dense medium. Angle of incidence approximately 42°. The beam bends away from the normal at an angle almost 90°.
Angle of incidence 45°. Total internal reflection occurs. The beam does not pass through.
Angle of incidence 60°. Total internal reflection occurs. The beam does not pass through.
Angle of incidence 75°. Total internal reflection occurs. The beam does not pass through.
Angle of incidence 85°. Total internal reflection occurs. The beam does not pass through.