Intriguing physics problem: photometry

Question

The question is: What is the intensity of illumination on the inner surface of the exposed spherical shell?

Condition: the size of the hole with a small radius "d" is much larger than the wavelength of visible light.

Task: In cloudy weather, we take measurements with a light meter facing the sky. We find that due to the light scattering of the cloud cover, the power incident on a unit surface has a value of "I" with a good approximation, regardless of the orientation of the light meter. There is a small hole with radius "d" on the top of an opaque, soot-covered, thin-walled spherical shell with radius "t".

Answer 1

Illumination is the art and science of lighting spaces to enhance visibility, aesthetics, and ambiance. Whether through natural sunlight, electric fixtures, or innovative technologies, illumination plays a crucial role in our daily lives. It can transform ordinary environments into extraordinary ones, influencing our mood, productivity, and overall well-being.

Properties of illumination

Understanding these properties is crucial in various domains, including architecture, photography, stage lighting, and interior design. Let us delve into these fundamental aspects of illumination:

1. Color Temperature: Color temperature measures the visual appearance of light, indicating whether it is warm or cool in nature.
2. Distribution: Distribution refers to the spread or direction of light in a space, achieved through specific lighting fixtures and techniques.
3. Direction: Direction of illumination defines the angle at which light falls on an object or surface, creating various effects and highlighting features.
4. Contrast: Contrast in illumination is the difference in light levels between different areas, resulting in pronounced shadows and dramatic effects.
5. Color Rendering: Color rendering measures how accurately a light source reproduces colors compared to natural sunlight, crucial in settings where color accuracy matters.
6. Energy Efficiency: Energy efficiency is essential in lighting, promoting the use of energy-efficient alternatives like LED bulbs to reduce consumption and increase lifespan.