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An observer looking across a swimming pool at point C views a light ray

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An observer looking across a swimming pool at point C views a light ray coming from a point A on the opposition side of the pool at the bottom. The ray leaves the water at a point 1.7 meters from opposition side of the pool and makes an angle of 45° degrees with the vertical. Thus the pool appears to be 1.5 meters deep.
 
Optics - An observer looking across a swimming pool - Physics Problems Optics - An observer looking across a swimming pool at point C views a light ray - Physics Problems
An observer looking across a swimming pool at point C views a light ray coming from a point A on the opposition side of the pool at the bottom. The ray leaves the water at a point 1.7 meters from opposition side of the pool and makes an angle of 45° degrees with the vertical. Thus the pool appears to be 1.5 meters deep. Find the pool true depth?
 
observer looking across a swimming pool at point C

First we apply Snell’s law and solve for the angle of incident Θ.
Snell's Law

Incident angle i = Θ and refractive angle r = 45°.

Refractive index n1 in water is 1.33 and refractive index n2 in air is one.
applying Snell's Law
Find incident angle
incident angle
incident angle

Incident angle is 32.1°.

From the geometry of the diagram, we see that
geometry

find true depth
depth
depth

d = 2.71 m

Pool true depth is 2.71 meters.
 
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