A typical fluorescent lamp is a little more than 1 m long and a few cm in diameter. How do you expect the light intensity to vary with distance (a) near the lamp but not near either end and (b) far from the lamp?

Fluorescent lamps are a ubiquitous sight in many settings, from schools and offices to homes and businesses. Unlike traditional incandescent bulbs, which generate light by passing electricity through a wire filament, fluorescent lamps utilize electricity to excite a gas, typically argon and mercury vapor, housed within a tube. Upon excitation, these gases emit ultraviolet light, which then strikes the phosphorescent coating on the inside of the tube, causing it to glow and produce visible light.

Due to their design, fluorescent lamps are known for their efficiency, converting more of their energy into light rather than heat, making them a popular choice for those seeking more energy-efficient lighting solutions. The tube-like shape of fluorescent lamps also creates a linear light source, as opposed to the single point of light emission found in traditional bulbs.

The inverse square law is a physical principle that describes the relationship between the intensity of a phenomenon and the distance from its source. When it comes to light, this law states that the intensity of light (or illumination) is inversely proportional to the square of the distance from the source. In mathematical terms, the intensity \( I \) is related to the distance \( d \) by \( I \propto \frac{1}{d^2} \).

In practical terms, this means that if you double the distance from a light source, the light intensity becomes one-fourth as strong. This principle plays a crucial role in understanding how light behaves as it travels and spreads through space, and is especially relevant when dealing with point sources of light.

A point source of light is an idealized light source that emits light uniformly in all directions from a single point in space. While no light source is a perfect point, this concept is a valuable model for understanding and calculating the behavior of light intensity.

In regard to the fluorescent lamp from the exercise, when a viewer is at a considerable distance from the lamp, it can approximate a point source. This is because, at large distances, the various angles from which light reaches the observer become less distinct, making the light source appear as if it is emitting from a singular point.

A cylindrical light source is a light-emitting body with a significant length compared to its diameter, resembling the shape of a cylinder. Unlike a point source, a cylindrical source spreads its light over its length, resulting in different light distribution characteristics.

With a fluorescent lamp, which acts as a cylindrical light source when observed up close, the intensity of light along the middle section of the lamp tends to remain relatively constant. The physical length of the lamp allows light to be distributed over a larger surface area, reducing the intensity fluctuation that would be experienced if the lamp were viewed as a point source. This accounts for the observation mentioned in Step 1 of the solution, where the light intensity near the lamp is less subject to the inverse square law and stays more consistent.