Brewster  Angle

4th July 2000

To make these pictures a piece of paper was placed under a horizontal microscope slide glass.  A white card was place vertically behind the slide and above it.  This card was illuminated by a flash gun, providing bright source of light which the glass reflected into the camera.  The flash was prevented from lighting the subject directly by a large lens hood, the shadow of which can be seen.  The camera was held at about the Brewster angle relative to the slide.  In the lower picture a polaroid filter was used.  The difference in the amount of reflection is very striking.  In theory the light is completely polarised at the Brewster angle.  In practice a photograph always subtends a finite angle, and so not all of it can be at the exact angle required . Furthermore, because the refractive index of light varies slightly with wavelength, the Brewster angle varies slightly with colour.  If the refractive index of the medium is R the Brewster angle measured from the normal to the surface is given by the formula B = tan^-1 R.  

When the incident light is at the Brewster angle, the refracted rays and the reflected rays are at right angles, and this is why the polarisation is complete.  In a sense, the reflected light is generated by the motion of electric charges in the glass.  These motions are at right angles to the rays of light in the glass. Motions at right angles to the plane of all the rays can always generate reflected light . But motions in the plane of the rays are somewhat along the direction of the reflected light.  Light cannot oscillate along its direction of motion – only sideways.  At the Brewster angle, the charges vibrating in the plane of the rays are exactly along the direction of the reflected light, which is therefore polarised entirely at right angle to the plane of the rays.

The partial polarisation of light from an insulating surface, such as a wet road, makes polaroid spectacles very efficient in reducing glare.