Calculating Apparent Depth: Air vs Water

[Alyce777]

Homework Statement

Instead of calculating apparent depth (for example, a penny in a glass of water appears to be closer to the surface than it actually is), instead of finding the angle of refraction and using snell's law, can I use the following:

Apparent Depth = Actual Depth x (n air / n water)
?

 

[G01]

Yes, that relationship will work for this situation. It comes ultimately from applying Snell's Law and the small angle approximation to the given problem.

 

[m2003]

I would say that while this formula may provide an estimation of apparent depth, it may not accurately reflect the true relationship between actual depth and apparent depth in air vs water. Snell's law takes into account the change in speed of light as it passes through different mediums, while this formula only considers the refractive indexes of air and water. Additionally, other factors such as the shape and curvature of the container, as well as the angle at which the object is viewed, can also affect apparent depth. Therefore, it is important to use a more comprehensive approach, such as Snell's law, to accurately calculate apparent depth in different mediums.