How Can Snell's Law Help Calculate Apparent Depth in Water?

In summary, to approach the problem of finding the apparent depth of a pond, you can use Snell's law of refraction and consider the rays emanating from a point source a distance below the surface. By examining the refraction of these rays and using trigonometry, you can find the relation between the real depth and the apparent depth, which is equal to the refractive index of the water.
  • #1
sphyics
102
0
Any help how to approach this problem.

The depth of pond is 10m. What is the apparent depth for a person looking normally to the water surface? ( Refractive index )water =4/3.
 
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  • #2
Make an attempt.
 
  • #3
i solved it by using the forumale (real depth/ apparent depth ) = refractive index

aparent depth comes out to be 7.5m.

My problem is how to get the relation
(real depth/ apparent depth ) = refractive index
 
  • #4
Use Snell's law of refraction and a little trig. (Examine the rays emanating from a point source a distance d under the surface. See how those rays refract. Consider small angles directly above the source.)
 
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1. What is the definition of apparent depth of water?

The apparent depth of water refers to the depth of a body of water as it appears to an observer, rather than its actual depth. It is affected by factors such as refraction of light, density of the water, and the angle of viewing.

2. How is the apparent depth of water different from the actual depth?

The actual depth of water refers to the distance from the surface of the water to the bottom of the body of water. The apparent depth, on the other hand, is the perceived depth of the water from an observer's point of view, which may not always be the same as the actual depth due to various factors.

3. What is the role of refraction in determining the apparent depth of water?

Refraction is the bending of light as it passes through different mediums, such as air and water. This phenomenon can make objects appear to be in a different position than they actually are, which affects the apparent depth of water when viewed from above.

4. How does the density of water affect the apparent depth?

The density of water plays a role in determining the apparent depth as it affects the refraction of light. Water with a higher density will cause light to bend more, making the apparent depth appear greater than it actually is. Similarly, water with a lower density will cause less refraction, resulting in a smaller apparent depth.

5. Does the angle of viewing affect the apparent depth of water?

Yes, the angle of viewing can significantly impact the apparent depth of water. When viewed at a shallow angle, the apparent depth can appear greater than it actually is, while viewing at a steeper angle can make the apparent depth seem smaller. This is due to the refraction of light and how it is affected by the angle of incidence.

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