The Disappearing Finger

I've got a question about optics: My son and I would like to understand an optical quirk we noticed with a rectangular aquarium. When we press a finger against the outer glass side of an aquarium it is visible when viewed from the adjacent (perpendicular) side only when it is pressed on the glass above the water level, but not when pressed below the water level. Can you help us understand why? Thank you!
- aaron (age 39)
Michigan, USA

Dear Aaron and son,

Congratulations!  You have independently rediscovered the phenomenon of the critical angle of reflection.

The technical reason is due to the fact that when a light ray traveling in a medium with index of refraction n₁ hits a boundary of a medium with an index of refraction of n₂ the relationship n₁sin θ₁ = n₂sin θ₂ holds between the angles and indices of refraction.  θ₁ is the angle of the incident beam and  θ₂ is the angle of the transmitted beam.   Solving for θ₂  you get sin θ₂ = n₁/n₂ * sin θ₁ .   This becomes nonsense when n₁/n₂ * sin θ₁ becomes greater than one.   So you get total internal reflection with no transmission.

Here is an experiment you can do.   Take a cylindrical water glass and fill it half full.  Hold the glass between a vertical pencil and your eye.  As you move the pencil back and forth you can see the two images moving and and a certain point the one going through the water vanishes. 

More info at 

All the best,

 

LeeH

 

 

 

 

(published on 11/19/2013)