Terms and Photometry

The branch of physics which deals with the quantitative measurement of light is called photometry. Light is either emitted from a source or is reflected from an object. Most of the objects are seen after reflection of light but some objects such as electric lamps, stars, sun, candle flame etc are seen by light emitted themselves.

Terms and Photometry

Luminous Flux

A source of light emits radiation of wide wavelength range. In photometry, we deal only with luminous energy, i.e. visible light which produces the sensation of vision, but not the other radiations it may emit. The amount of light energy emitted by a source per second is called luminous flux. It is denoted by Q. its unit is the lumen. This is a part of the total radiation from a light source which can affect the eye.

Lumen

Lumen is the unit of luminous flux and is defined as the amount of luminous flux emitted per unit solid angle by a point source of is candle power.

Luminous Intensity

Luminous intensity is defined as the amount of luminous flux emitted by a source per unit solid angle, \(\omega\) in that direction. It is also known as illuminating power and is denoted by L. If Q is the amount of luminous flux emitted by a source uniformly in all directions, then the luminous intensity is

\begin{align*} L &= \frac {Q}{\omega } \\ \text {or,} \: L &= \frac {Q}{4\pi } \dots (i) \\ \end{align*}

Where ω is the solid angle and at the centre of a sphere ω = 4π.

Its unit is lumen per steradian or simply candela, cd. Equation (i) is the relation between luminous intensity and luminous flux.

Intensity of Illumination

The amount of light energy incident on unit area of a surface per second is called intensity of illumination. In other words, it is defined as the luminous flux falling normally per unit area of the surface held at that point. It is also called illumination or luminance of surface and is denoted by I.

Let us consider a source of light placed at the centre of a hollow sphere of radius r. If Q is the amount of light energy emitted per second by the source and 4\(\pi\)r² is the area covered by the light energy, then from definition, we can write,

\begin{align*} I &= \frac {Q}{A} \\ \text {or,} \: I &= \frac {Q}{4\pi r^2} \dots (i) \\ \text {Again, from luminous intensity, we have} \\ L &= \frac {Q}{4\pi } \\ I &= \frac {Q}{4\pi r^2} \\ \text {So equation} (i) \text {becomes} \\ \end{align*}I

$$I=\frac{L}{r^2}$$

This is a relation between theintensity of illumination of a surface and luminous intensity of a source. Since L is constant, so

$$I \propto\frac {1}{r^2} $$

This shows that the intensity of illumination of a source at a point is inversely proportional to the square of the distance from the source of light. This is known as the inverse square law of photometry. The unit of intensity of illumination is phot in CGS-system and lux in SI-units.

Phot or Centimeter Candle

It is the amount of light energy falling normally on a square centimeter spherical surface of radius one centimeter when a source of one candle is kept at the centre of the sphere i.e. one phot = one lumen per square centimeter.

Lux or Metre Candle

It is the amount of light energy falling normally on a square meter spherical surface of radius one metre when a source of one candlepower is kept at the centre of curvature i.e. one lux = one lumen per square meter.

$$1 \text {phot} = 10^4 \text {lux} $$

Inverse Square Law

Consider a pint source of light S which is emitting light in all direction uniformly. Let the light energy emitted per sec by the source is Q. Draw two spheres of radius r₁ and r₂ as shown in the figure. Then the illumination of area 4\(\pi\)r₁² and 4pr₂² are

\begin{align*} I_1 &= \frac {Q}{4\pi r_1^2} \dots (i) \\ I_2 &= \frac {Q}{4\pi r_2^2} \dots (ii)\\ \text {Dividing equation} (i) \text {by equation} (ii), \text {we get} \\ \frac {I_1}{I_2} &= \frac {Q}{4\pi r_1^2} \times \frac {4\pi r_2^2} {Q} \\ \frac {I_1}{I_2} &= \frac {r_2^2}{r_1^2} \\ \text {In general,} \\ I &\propto \frac {1}{r^2} \\ \end{align*}

Thus the intensity of illumination of a point is inversely proportional to the square of the distance from the source.