Decrease in intensity of light on undergoing successive reflections

[Amith2006]

Sir,
1) A thick plane mirror shows a number of images of the filament of an electronic bulb. It is said that of these images the first image is the brightest. Is it true? If so, is it because some energy is lost in traversing through the dense medium?
2) It is said that the intensity of light at a large distance r from a long, thin cylindrical source of light is proportional to r^0. Is it true? I know that intensity of a point source is proportional to r^(-2). In what way is a long, thin cylindrical source of light different? Can't the cylindrical source be treated as a point source for large distances? Here the symbol ^ stands for power.

 

[Astronuc]

1) Some light is scattered within the solid medium and at the interface of the solid and atmosphere. So some intensity (number of photons) is lost.

2) A line is essentially a continuous series of point sources, and each contributes to the light being received at some distance. If one does the integral, then one sees that the light intensity is inversely proportional to the distance r (or r^-1) from the line.

Keep in mind this applies to a very long line, which is observed along a line perpendicular to the line of light sources.

If the line is short, then the intensity would approach that of a point source a long distance.

Also the orientation (angle) of the 'short' line with respect to the line of observation would have to be considered.

 

[kyle8921]

1) It is true that the first image formed by a thick plane mirror will be the brightest. This is because as light reflects off of the surface of a mirror, some of its energy is absorbed and converted into heat. This results in a decrease in intensity of the reflected light with each successive reflection. Therefore, the first image, being the closest to the original source of light, will have the highest intensity.

2) It is not entirely accurate to say that the intensity of light at a large distance from a long, thin cylindrical source is proportional to r^0. While it is true that the intensity of a point source is inversely proportional to the square of the distance, the intensity of a cylindrical source is dependent on both the distance and the angle at which the light is received. This is because a cylindrical source emits light in a cylindrical shape, rather than a point source emitting light in all directions. Therefore, the intensity of light from a cylindrical source will decrease with distance, but not at the same rate as a point source. It is not appropriate to treat a cylindrical source as a point source for large distances, as the distribution of light is different.