Interview Questions Reloaded

[shinichi9htv]

Originally Posted by shinichi9htv

It looks like Bougerol's indetity

bro bro, Bougerol's identity is only a special case of your prob when v=0 huhu. Please give the answer for this interesting question.

[dexter8310]

Originally Posted by Khoa Tran

Here's a fun Physics question to ask during an interview.

Everyone knows that a light ray is reflected in the direction symmetric to the incident ray, with respect to the normal (like in the figure below).



However, the incident ray hits the surface at only one point, say O. Suppose that we rotate the plane around O an angle . The incident ray is the same and the hit point O is the same. But the reflected ray changes. Why is that?

[You may ask the same question with the motion of a super-tiny ball.]

The key point here is 2 rays are symmetric through the normal plane, not the point O.
If this is a finance interview, I would answer that your expected return will change when the market situation changes. But I doubt they would ever ask this.

[Khoa Tran]

Originally Posted by dexter8310

The key point here is 2 rays are symmetric through the normal plane, not the point O.
If this is a finance interview, I would answer that your expected return will change when the market situation changes. But I doubt they would ever ask this.

Well, I think the point of the question is why the plane affects the reflection while the ray/ball hits it at only 1 point

[dexter8310]

Originally Posted by Khoa Tran

Well, I think the point of the question is why the plane affects the reflection while the ray/ball hits it at only 1 point

Exactly why the question is raised: which plane? If you turn the intersection plane without changing its normal line, there won't be any change to the reflection ray, no matter what.

[YADD]

Genius! Genius...

Shockingly beautiful. The explanation (Hugens' wave or Newton's particle) is irrelevant; it's more about an insightful observation being made.

[Khoa Tran]

Originally Posted by YADD

Genius! Genius...
Shockingly beautiful. The explanation (Hugens' wave or Newton's particle) is irrelevant; it's more about an insightful observation being made.

Can you explain more how you find it shockingly beautiful? It's possible that my way of seeing it, which is also deadly simple (i.e. Newton's third law), is different from yours.

[YADD]

The acute observation means that the reflection and refraction effects are non-local.

For the reflection part, two possible yet equally satisfactory explanations: (1) Newton's particle picture - light is a beam of particles bouncing off a surface; the normal component of velocity reverses; (2) Huygens's wave picture - light is a motion of wavefronts in an ether.

As a detour: For the refraction part, there is a key difference between the two theories. (1) Newton demanded that the light particles are attracted by the medium (think about his law of gravity!) => light moves faster in matter => the light beam gets bent downward. (2) Huygens: matter slows down the beam! => wavefronts change direction such that the beam turns downward. (Some pictorial drawings needed here, I'll skip them.)

This difference is falsifiable. Not until the advance of optical measurement in the 19th centary did Fizeau establish the evidence of slowing down of light in water.

Having studied physics for many years, it was my negligence till your post failing to have recognized two things: (a) By logics alone, Newyon's particle picture was less satisfactory/natural with regard to refraction (detailed below); (b) How does matter slow down light?

(a) In Huygens picture, wavefronts get slowed down everywhere in the medum. In Newton pictute, the light beam gets a "kick" up in speed only around the vicinity of the medim/vacuum interface. Once light enters into the medium, "attractive forces" on the light partciles are balanced in all directions and the partciles thus continue on a straight line acording to 1st Newton law. While not illogical, this explanation is forced and less natural.

(b) Now we know a medium is mostly an empty space. How does it take more time for light to travel an alike distance? Maxwell's EM theory is descriptive by means of an effective refraction index; the theory is not explanatory. A fancier theory is needed (QED, perhaps thru absoption and re-emission???). While confident that the effect must have been addressed in QED (and quantum optics), I am surprised at my own negligence/overlooking of the subject.

[HungQNguyen]

Yeah, I absolutely agree with you that the effects are non-local. In fact, we often missed the striking beauty of this phenomenon. Newton's picture and Huyghen's picture also differentiate when the interface of 2 media is no longer infinitely large but come down to dimension comparable to wavelength.