Light is nothing but the electromagnetic waves of wavelengths within a specific range which can create vision sensation to the human eyes. Maybe there are some electromagnetic waves of different wavelengths which can create a sensation to other animal’s eyes. But we do not consider them as light energy. Because they do not create any sensation to the human eyes.
Flux of Light or Luminous Flux
The flux of Light or Luminous Flux is the light energy radiated from a hot body per second. This is the rate at which the energy propagates. So, the flux of light is in the form of power. The unit of this flux is lumen. One lumen is the amount of flux of a standard candle passing through one unit of solid angle.
Again, as per the definition of a standard candle, we know that a standard candle is the source of light energy which radiates light of one candle power.
The Relation between Candle-Power and Lumen
Before establishing this relation we have to recall the basic concept of a solid angle.
For that let us consider a surface area of A square meter. Also, we will consider that this surface area is the part of the sphere of radius r meter. Then the solid angle subtended at center C of the sphere is
Now the enter surface area of the complete sphere is
Hence, the total solid angle of the sphere is
Since, the lumen is nothing but the flux emitted per unit solid angle by a source of one candle power or a standard candle, the radiated light from one candle power or standard candle is
AgainHence, we can say
Suppose there is a light source. The source is radiating light of F lumens towards a particular direction. Also, we will imagine the light covers a certain surface area of an object. This area creates a solid angle ω with respect to the center of the source of light. The luminous intensity or candle power is the ratio of the luminous flux in lumens to the solid angle in steradian.
We can define the luminous intensity as the luminous flux emitted by a light source per unit solid angle. We generally denote the luminous intensity with the capital letter I.
If a light source emits light with equal intensity towards all directions, total luminous flux emitted by the light is
Average Luminous Intensity
Mean Spherical Candle Power
It is not mandatory to have the same intensity of light in all directions of a light source. It is the reason we generally use average candle power or average luminous intensity instead of actual candle power or actual luminous intensity. We determine the average luminous intensity by dividing total luminous flux emitted from the light source by 4π. Since 4π is the total solid angle around the source. Also, we call this average candle power or average luminous intensity as Mean Spherical Candle Power.
The candle is the unit of luminous intensity. This is the very basic unit of a quantity related to illumination. One candle is 1/60th of luminous intensity per centimeter square of a black body radiator at the temperature of solidification of Platinum.
The illumination flux illuminates the surface of an object when it falls on the object. We measure illumination of a surface by luminous flux falls on that surface per unit area. If F is the luminous flux falls on area A of the surface of an object. Then we can write the illumination as
Since the unit of luminous flux is lumen and the unit of area in square meter, we can write the unit of illumination as lumen per square meter.
Now one candle power is the same as 4π lumen. Again a sphere has total surface area is 4πr. Where, r is the radius of the sphere. Now if r is 1 m then the surface area of the sphere is 4π. Again, 1 candle power is 4π lumens. Hence, the illumination of the inner surface of the sphere of 1 m radius around the light source of one candle power is one lumen per meter square. And this is why we also referred to the unit of illumination as meter candle. Also, we refer to this unit of meter candle as lux.