Optics question - coin at the bottom of a swimming pool

In summary, The apparent depth of a coin at the bottom of a swimming pool filled with water (n=1.33) to a depth of 2.16m depends on the angle of viewing. To find the apparent depth when viewed at near normal incidence, the formula dapp = tan(theta1) / tan(theta2) * d can be used. For rays that leave the coin at an angle of 35.0 with the normal to the bottom of the pool, theta2 can be calculated using Snell's law.
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Optics question -- coin at the bottom of a swimming pool



The apparent depth of a pool depends on the angle of viewing. Suppose that you place a coin at the bottom of a swimming pool filled with water (n = 1.33) to a depth of 2.16m.
Find the apparent depth of the coin below the surface when viewed. a) at near normal incidence nd b)By rays that leave the coin making an angle of 35.0 with the normal to the bottom of the pool.


I solved part a but for part b what I don't understand is don't we need to know theta2 aswell
like here we know that


dapp = tan(theta1) / tan(theta2) * d;

where d is 2.16 and theta 1 = 35.0 don't we need to know theta2 to solve this ?
 
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  • #2


Can't you use Snell's law to calculate theta2?
 

FAQ: Optics question - coin at the bottom of a swimming pool

How does the coin appear to the human eye at the bottom of a swimming pool?

The coin will appear to be closer to the surface and larger than its actual size due to the refraction of light in water. It will also appear slightly distorted and may appear to be at a different location than where it actually is.

Why does the coin appear closer and larger?

This is due to the phenomenon of refraction, where light bends as it passes through different mediums, in this case, from water to air. The bending of light causes the image of the coin to appear closer and larger than its actual size.

How does the depth of the pool affect the appearance of the coin?

The deeper the pool, the greater the refraction of light and the stronger the distortion of the image of the coin. This is because there is a larger distance for the light to travel and bend before it reaches the human eye.

What other factors may affect the appearance of the coin at the bottom of a swimming pool?

The clarity of the water, the angle at which the coin is viewed, and the presence of any obstructions or shadows can also affect the appearance of the coin. Additionally, the shape and size of the coin can also impact how it is perceived by the human eye.

Can the same phenomenon be observed with other objects besides a coin?

Yes, any object placed at the bottom of a swimming pool will exhibit similar refraction and distortion. The closer the object is to the surface, the more pronounced the effect will be. This phenomenon can also be observed in other transparent mediums, such as glass or plastic.

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