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when the submarine is at some depth 'h' and emits an circular area of light with radius r. if the submarine goes down with depth 2h, then what effect would it have on the area of circular light on the surface of water ?

wil it widen or diminish?

When a submarine emits a circular area of light at a certain depth, the behavior of that light as the submarine descends deeper into the water is quite interesting. To understand the effect on the area of the circular light at the surface when the submarine goes from a depth 'h' to '2h', we need to consider how light behaves in water and how depth affects the spread of that light.

Understanding Light Propagation in Water

Light travels in straight lines, but its intensity and visibility can be affected by the medium it travels through. In water, light can be refracted, absorbed, and scattered. As the submarine goes deeper, the light emitted will still travel upwards, but the distance it can effectively illuminate will change.

Analyzing the Situation

Let’s break this down step by step:

• At Depth 'h': When the submarine is at depth 'h', the light creates a circular area of illumination on the surface with a radius 'r'. This means that the light reaches the surface and forms a circle with that radius.
• At Depth '2h': As the submarine descends to depth '2h', the light still travels upwards, but it has to cover a greater distance. The key factor here is the angle at which the light spreads as it travels through the water.

Geometric Considerations

To visualize this, think of the light as emanating from a point source at the submarine. The light rays will diverge as they move away from the source. The deeper the submarine goes, the larger the angle of divergence becomes, but the effective radius of the light circle on the surface will be influenced by the depth.

Using basic geometry, we can see that if the submarine is at depth 'h', the radius 'r' of the light circle can be thought of as a function of the angle of divergence and the depth. When the submarine goes to '2h', the distance the light has to travel doubles, which means the same angle of divergence will result in a larger radius on the surface.

Conclusion on the Effect of Depth

As the submarine descends from depth 'h' to '2h', the area of the circular light on the surface will actually widen. This is because the light rays, while still diverging, have more distance to spread out before they reach the surface. Therefore, the radius of the illuminated area increases, leading to a larger circle of light on the water's surface.

Final Thoughts

In summary, the deeper the submarine goes, the larger the area of light on the surface becomes due to the increased distance the light travels and the angle at which it spreads. This phenomenon illustrates how light behaves in different mediums and how depth can significantly affect visibility underwater.