Question 1: Define the inverse square law and explain its significance in the context of light intensity and photosynthesis.

Answer: The inverse square law states that the intensity of light or other radiative energy from a point source decreases proportionally to the square of the distance from the source. It is significant in photosynthesis because it influences how much light energy reaches plants at different distances, affecting their ability to carry out photosynthesis efficiently.

Question 2: Describe how the inverse square law would affect the design of artificial lighting systems used in controlled plant growth environments.

Answer: Artificial lighting systems must account for the inverse square law by positioning lights at appropriate distances to ensure uniform light intensity across the plants. As distance increases, light intensity decreases rapidly, so lighting arrangements are designed to optimise energy use and plant growth.

Question 1: A light source emits an intensity of 1000 lux at a distance of 2 metres. What is the intensity of the light at 8 metres? (Use the inverse square law formula: I₁ / I₂ = (d₂ / d₁)²)

Answer: I₂ = 1000 × (2 / 8)² = 1000 × (1/4)² = 1000 × 1/16 = 62.5 lux

Question 2: A solar panel receives an intensity of 600 W/m² at 1.5 metres. If the panel is moved to 4.5 metres, what is the new intensity?

Answer: I = 600 × (1.5 / 4.5)² = 600 × (1/3)² = 600 × 1/9 = 66.67 W/m²

Question 1: Outline a simple experimental setup to investigate how light intensity from a point source varies with distance. Include the key variables involved and safety precautions.

Answer: An experiment could involve a fixed light source and a light sensor or lux meter placed at various distances (e.g., 1m, 2m, 3m, etc.) from the source. Independent variable: distance from the source; dependent variable: measured light intensity. Control variables: same light source, same environmental conditions. Safety precautions include avoiding direct staring into bright lights, ensuring the power supply is safe, and handling equipment carefully to prevent damage or injury.

Question 1: A research team measures the light intensity at various distances from a lamp used in a greenhouse. The data shows that at 1 metre, the intensity is 800 lux; at 2 metres, it is 200 lux; at 4 metres, it is 50 lux. Analyse this data and explain whether it supports the inverse square law.

Answer: The data shows that when the distance doubles from 1m to 2m, the intensity decreases from 800 lux to 200 lux, which is a factor of 4. Similarly, increasing the distance from 2m to 4m doubles it again, and the intensity drops from 200 lux to 50 lux, which is also a factor of 4. This pattern supports the inverse square law, as intensity decreases proportionally to the square of the distance.

Question 1: Explain how the inverse square law influences the design of artificial lighting in horticultural industries. Discuss the importance of correct positioning and how it impacts plant growth efficiency.

Answer: The inverse square law states that light intensity decreases rapidly as distance from the source increases. In horticultural industries, artificial lights are positioned at specific distances to ensure plants receive adequate and uniform light. Proper positioning minimizes energy wastage and maximises photosynthesis, leading to healthier plant growth. Incorrect placement can result in uneven growth or energy inefficiency. Understanding this law helps engineers optimise lighting setups for commercial plant production.

Question 1: Describe how engineers designing solar-powered systems must consider the inverse square law when positioning solar panels for optimal energy capture, especially in large-scale solar farms.

Answer: Engineers must position solar panels at distances and angles where light intensity is maximised. Since light intensity decreases with the square of the distance from the sun (or other sources), understanding this law helps in designing layouts that maximise energy absorption, especially in large-scale solar farms where optimal positioning can significantly improve efficiency and energy output.