Optics

Refraction of light, refractive index

When light crosses a boundary between transparent media, its speed and usually its direction change. The refracted ray bends at the interface.

When light crosses a boundary between transparent media, its speed and usually its direction change. The refracted ray bends at the interface.

Law and application

Quick check

When light passes from air into water, its speed decreases and the refracted ray bends toward the normal; in the reverse direction it bends away. Snell’s law is $n_1\sin i=n_2\sin r$, with angles measured from the normal and refractive index $n=c/v$. For air-to-glass, take npprox1.5: an incidence angle of $30^\circ$ gives \sin rpprox0.33, so rpprox19^\circ. A spoon partly immersed in water appears bent because refraction shifts the apparent position of its submerged part.To predict the direction, draw the normal at the interface first, then place the refracted ray on the other side; a ray entering perpendicular to the boundary does not change direction.

Refractive index is the ratio of light speed in vacuum to its speed in a medium, not the medium’s brightness or amount of matter. At a boundary, light frequency remains unchanged because it is set by the source; speed and wavelength change together according to $v=f\lambda$. Thus wavelength is shorter in glass than in air even though the colour does not change. When a ray travels from higher to lower index, Snell’s law predicts an incidence angle at which the refracted ray grazes the boundary. This is the threshold for total internal reflection.