Light traveling from material 1 to material 2 is incident on material 2’s surface at an angle qi, as shown above. If materials 1 and 2 have the same index of refraction, which path will the light take upon refraction?
I used this question, adapted from an AP-style question in the newest edition of Serway, on a recent quiz. I don't think anyone in my class missed it. Most folks answered it conceptually: they know that light bends toward the normal when slowing down at an interface, away from normal when speeding up. They correctly split the difference, recognizing that without a speed change there's no refraction. A few used Snell's law, knowing that with equal n's, equal thetas are required.
Then I asked, what is the physical manifestation of this quiz?
Consider a beaker of water, as shown above. If I were to put a clear (not cloudy) ice cube in the water, how would we know that the ice cube was there? Well, the water would look distorted at the location of the ice, because ice has a different index of refraction than water. The bending of light at each face of ice would provide visual cues that something is inside the water.*
* Well, that and the fact that the ice would float on top of the water. But still.
But what if I were to dunk an object with the same index of refraction as water? What would I see?
Based on the quiz, the class reasons through the question: rays of light would not bend at any interface. Even a laser would pass straight through the object undeflected. So we would see nothing.
A few years back, chemistry professor Pam Kerrigan of the College of Mount St. Vincent introduced me to Ghost Crystals. (Follow the link for one place to purchase them, or ask your chem department.) You place them gently in distilled water overnight, and they grow by absorbing water. In their fully engorged state, they are solid, but have the same index of refraction as water. Thus, when you place them in a beaker of water, they disappear -- just like we predicted on the quiz.
Now, the trick is, I've showed the students the "empty" beakers with a discussion of what would happen "if" I were to place a ghost crystal inside one and wait a day. But after I do so, I reach in... and remove the engorged ghost crystal that no one noticed was already inside. See -- there it is, now, out of the beaker on the desk.
I've seen (and done) this demo with Pyrex and mineral oil. I think it's actually more impressive that way, especially if you throw a broken test tube into the beaker and remove the (already prepared) intact test tube that was previously invisible. But mineral oil is messy messy messy, and I don't feel like paying for dry cleaning every time I do this demo. So I went to ghost crystals.