Authors' Mistakes #24 - CSI Miami (Marc Dube)

I confess: I am a fan of CSI Miami.  I don't like the CSI series located in Las Vegas and New York.  But the Miami series is bathed in warm colours and shows beautiful scenery.  I know that it was actually filmed in California and that the warm feel was obtained by saturating the colours, but who cares?  I also find the characters reasonably appealing.

Anyhow, last night I discovered a mistake in episode 16 of season 7 (Sink or swim).  I am not referring to the many licences that the authors take with the way CSI people operate in real life.  I understand that if our fictitious CSIs were confined to the labs and spend days to analyse a sample, the stories would evaporate.  What they did in Sink or swim violated the laws of Physics!

Here it goes.
An assassin kills a lady standing at the railing of a yacht by shooting her from underwater.
Do you see no problem with that?

There is one: when a ray of light crosses the boundary between water and air, it changes direction.  This phenomenon is called refraction (see for example the refraction page on Wikipedia).  Here is a nice diagram (also from Wikipedia) to describe it:

Suppose that the top side is air (with refractive index n₁ = 1) and the bottom side is water (with refractive index n₂ = 1.33).  Snell's law tells you that sin(θ₂) = sin(θ₁) * n₁ / n₂.  This means that light entering the water with an angle of, say 30°, is deflected to approximately 22°.  As a result of the deflection, the underwater shooter of CSI Miami saw his target 8° higher than it was.  With a target placed, say, 5 metres above the water, 8° roughly correspond to more than 80 cm.  Enough to shoot above the target's head instead of hitting her heart.  The effect increases when the angle increases.  So, for example, with θ₁ = 45°, θ₂ becomes 32°, which is 13° less than θ₁.

Obviously, the positions of both the target and the shooter also play a crucial role.  For example, the 80 cm of the previous calculation are reduced to 49 cm if the target is only 3 m above the water instead of 5.

Now, refraction has no impact if the shooter is directly below the target, because both angles become zero.  But this is not what happened in CSI Miami, as the shooter had to be somewhat away from the boat in order to clearly see his target.

All in all, there is no way that the shooter could have made the kill.

Funnily enough, the Archerfish manages to hit insects one or two metres above the water by spitting at them from underwater.  A thorough study about that fish was published by Lawrence M. Dill in 1977 (Refraction and the Spitting Behavior of the Archerfish (Taxotes chatareus), Behavioral Ecology and Sociology, 2, 169-184).

For your reference, here are the links to all past “Authors’ Mistakes” articles:
Lee Child: Die Trying
Colin Forbes: Double Jeopardy
Akiva Goldsman: Lost in Space
Vince Flynn: Extreme Measures
Máire Messenger Davies & Nick Mosdell: Practical Research Methods for Media and Cultural Studies
Michael Crichton & Richard Preston: Micro
Lee Child: The Visitor
Graham Tattersall: Geekspeak
Graham Tattersall: Geekspeak (addendum)
Donna Leon: A Noble Radiance
007 Tomorrow Never Dies
Vince Flynn: American Assassin
Brian Green: The Fabric of the Cosmos
John Stack: Master of Rome
Dean Crawford: Apocalypse
Daniel Silva: The Fallen Angel
Tom Clancy: Locked On
Peter David: After Earth
Douglas Preston: Impact
Brian Christian: The Most Human Human
Donna Leon: Fatal Remedies
Sidney Sheldon: Tell Me Your Dreams
David Baldacci: Zero Day
Sidney Sheldon: The Doomsday Conspiracy