To estimate how much brighter the Sun would need to be to illuminate the bottom of the ocean, we need to consider the factors that affect the penetration of light in water.
Water absorbs and scatters light, and as light travels deeper into the ocean, it becomes progressively attenuated. The attenuation is influenced by various factors, including water clarity, suspended particles, dissolved substances, and depth.
The average depth of the world's oceans is approximately 3,800 meters (12,500 feet). At this depth, only a small fraction of sunlight reaches, and the illumination is extremely dim. To make the bottom of the ocean as bright as, let's say, the surface of the land on a sunny day, we would need to significantly increase the amount of light reaching the depths.
Assuming we want the same level of brightness at the bottom of the ocean as on land, we can make a rough estimation. The surface of the land is illuminated by direct sunlight, which has an intensity of about 100,000 lux on a sunny day.
To increase the brightness at the bottom of the ocean, we would need to account for the attenuation of light as it travels through the water. The attenuation coefficient varies depending on water conditions, but let's assume a relatively clear ocean with an attenuation coefficient of 0.05 per meter.
If we consider an average depth of 3,800 meters, the total attenuation would be 0.05 x 3,800 = 190. This means the light intensity would be reduced by a factor of 190.
To compensate for this attenuation and achieve the same brightness as the surface of the land, the Sun would need to be approximately 190 times brighter at the surface of the ocean compared to its current brightness.
However, it's important to note that this is a simplified estimation, and the actual brightness required could vary based on different factors, such as local conditions, water properties, and the desired level of illumination.