A teacher sets up the following demonstration in which he places a clear glass rod with an index of refraction of 1.47 into a beaker containing an unknown liquid. When he does this, the submerged portion of the glass rod seems to disappear. The teacher gives the students the following list of possible liquids in which this glass rod has been submerged. Material Index of Refraction
Salt Water 1.37
Glycerin 1.47
Silicon Oil 1.52

Required:
Which material is most likely to represent the liquid in the beaker and why?

salt water

total internal reflection

Explanation:

Let's analyze this experiment, for the rod to disappear it must have happened that the light coming from it does not reach us that we are seeing from the air n = 1, therefore the light from the rod must be reflected, for this to happen we use the refractive ratio

           n₁  sin θ₁  = n₂ sin θ₂  

where n₁ is the refractive index of the rod, the greatest angle that could exist in the liquid is 90º, therefore sin 90 = 1

            n₁ sin θ₁  = n₂

           sin θ₁ = n₂ /n₁

the only way this expression is correct is that

             n₂ <n₁

that is

             n₂ < 1.47

When reviewing the given materials, the only one that meets this condition is salt water by the total internal reflection

an energy transformation flow diagram is shown

where is it ?

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y