### Photometric Definitions

*Q: What is the physics of light rays?*

To properly understand these discussions, we must be clear about the precise terms and ideas we are using and it is important to appreciate the physical laws and units of measurement. We give below a summary of these important terms and units.

ANGLE OF INCIDENCE

We use this when a ray of light travelling in medium 1, meets another medium 2. The angle of incidence is the angle between the light ray in medium 1 and and the normal (perpendicular) to the surface or boundary of medium 2.

INVERSE SQUARE LAW

All light is subject to the inverse square law which says that the energy is dissipated (spreads out) according to the square of the distance travelled. Thus,

energy E = 1/d2. A luminous intensity measured at a distance of 1 metre will reduced by 0.25 at a distance of 2 metres and 0.01 at a distance of 10 metres.

LUMINOUS INTENSITY

The unit of luminous intensity is called the candela, with the unit abbreviation cd. It is a base unit in the standard European system of measurements known as SI (Systeme Internationale). The candela is the luminous intensity in a perpendicular direction of a surface of 1/600,000 square metres of a full radiator at the temperature of freezing platinum under an atmospheric pressure of 1 Bar (101325 newtons per square metre).

The candela replaced the older unit known as the international candle, which was defined in terms of the light emitted per second in all directions from a specified electric light source. The conversion factor is

1 candela = 0.982 international candles

LUMINOUS FLUX

The unit of luminous flux is the lumen, abbreviated by the symbol lm. It is defined as the light energy emitted per second within unit solid angle by a uniform point source of 1 unit luminous intensity.

1 cd = 1 lm sr-1

ILLUMINANCE

The illuminance of a surface is defined as the luminous flux reaching it perpendicularly per unit area. The British unit is the lumen per square foot (lm ft-2), otherwise called the foot candle. The metric unit is the lumen per square metre (lm m-2), also called the lux (lx).

LAMBERTS COSINE LAW

When a surface receives light obliquely, the illumination is proportional to the cosine of the angle of incidence.

LUMINANCE

The luminance of a surface is the measure of the light actually emitted per unit area of that surface, the plane of projection being perpendicular to the direction of view. The unit is candelas per square metre (cd m-2).

REFRACTIVE INDEX

The refractive index, n, of a material is the ratio of the velocity of light in a vacuum (free space) to the velocity of light in the material.

Thus, n(glass) = v(space) / v(glass)

SNELL'S LAW

For light incident upon a boundary between two media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. This constant is equal to the inverse ratio of the refractive indices of the two media.

Sin(i)/Sin(r) = n(medium 2)/n(medium 1)

DIOPTRE

A dioptre is the unit of measure of the power of a lens and is the reciprocal of its focal length, expressed in metres.

Thus, if the focal length of a lens = 0.50 m, then its power = 1/0.5 = 2 dioptres.