The ratio of real depth to apparent depth is equal to the refractive index of the medium.
This relationship arises due to the phenomenon of refraction, where light bends as it passes from one medium to another. When we observe an object submerged in a medium (like water), it appears to be at a shallower depth than its actual depth. This perceived depth is the apparent depth.
Here's a breakdown:
- Real Depth: The actual vertical distance of the object from the surface of the medium.
- Apparent Depth: The depth at which the object appears to be when viewed from a different medium (usually air).
- Refractive Index (n): A measure of how much light bends when passing from one medium to another. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.
Mathematical Representation:
The relationship can be expressed as:
Refractive Index (n) = Real Depth / Apparent Depth
Therefore:
n = Real Depth / Apparent Depth
Explanation:
- When light travels from a denser medium (e.g., water) to a rarer medium (e.g., air), it bends away from the normal. This bending makes the object appear closer to the surface than it actually is.
- The amount of bending depends on the refractive index of the two media. The higher the refractive index of the denser medium, the greater the bending, and the smaller the apparent depth will be compared to the real depth.
Example:
If a stone is at a real depth of 4 meters in a pool of water, and the refractive index of water is approximately 1.33, then the apparent depth can be calculated as:
Apparent Depth = Real Depth / Refractive Index
Apparent Depth = 4 meters / 1.33
Apparent Depth ≈ 3.01 meters
Therefore, the stone will appear to be at a depth of approximately 3.01 meters.
In summary, the refractive index provides a direct measure of how much shallower an object appears to be when viewed through a different medium than its actual depth, making the ratio of real depth to apparent depth a crucial factor in understanding refraction.
