Aswimming pool is filled to a depth of 2.0 m. how deep does the pool appear to be from above the water, which has an index of refraction of 1.33? (a) 1.5 m (b) 1.33 m (c) 2.5 m (d) 1.5 cm

(A) 1.5 m

Explanation:

This situation is due to Refraction, a phenomenon in which a wave (the light in this case) bends or changes its direction when passing through a medium with an index of refraction different from the other medium.  

In this context, the index of refraction is a number that describes how fast light propagates through a medium or material.  

In addition, we have the following equation that states a relationship between the apparent depth and the actual depth :  

(1)  

Where:

is the air's index of refraction

water's index of refraction.

 is the actual depth of water

Now. when is smaller than the apparent depth is smaller than the actual depth.   And, when is greater than the apparent depth is greater than the actual depth.  

Let's prove it:

(2)  

Finally we find the apparent depth of water, which is smaller than the actual depth: