Prisms

[MedPR]

If you have two light rays incident on a prism, shouldn't the one that refracts the most (bends the most towards normal) once it goes from air into the prism be the one with the smaller n?

I'm referring to example 10.6a in TBR physics. I don't have the image, but hopefully my explanation will suffice.

Two initially parallel visible light rays, A and B, are incident upon one surface of a prism. Which of the following is true regarding their wavelengths and wave speesd within the material

The image shows a triangular prism, with parallel rays A and B starting out in some medium (let's just say air).

When A enters the prism, it refracts some, say about 30deg. When it exits the prism, it refracts even more toward normal, probably about 45degrees below horizontal.

When B enters the prism, it doesn't refract at all. The ray inside the prism is parallel to the ray that entered the prism. When B exits, it refracts and bends toward normal at about 30degrees below horizontal.

The answer is that lambdaB > lambdaA, and velocity of B > velocity of A.

Explanation:

When two rays bend differently upon entering a new medium, their indexes of refraction must be different. The ray that bends more has a higher refractive index; Ray A has a higher n. Now, consider how th ewavelengths and speeds of th elight are affected within the prism. Because v=c/n, Ray A must move more slowly than Ray B. In the visible spectrum, light of higher frequency refracts more than light of a lower frequency. Given that vA is less than vB, for frequency to remain constant as a ra ychanges medium, lambdaA must be less than lambdaB.

I understand the relationship between n, v, freq, and wavelength (e.g I know that if lambdaB > A, then vB > A as well).

I'm not understanding this:

The ray that bends more has a higher refractive index

If you pass a ray of light from air into water, the ray will bend towards the normal when it enters the water, because water has a higher refractive index than air. In this problem, however, the refractive index of the mediums are the same for both rays. So if ray B doesn't bend as much as ray A when both pass from a lower refractive index medium into a higher refractive index medium, doesn't that mean that A started out with a lower refractive index compared to B?

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[milski]

I'm not understanding this:


If you pass a ray of light from air into water, the ray will bend towards the normal when it enters the water, because water has a higher refractive index than air. In this problem, however, the refractive index of the mediums are the same for both rays. So if ray B doesn't bend as much as ray A when both pass from a lower refractive index medium into a higher refractive index medium, doesn't that mean that A started out with a lower refractive index compared to B?

I am not completely sure exactly what you're asking here. The rays themselves don't have a refracting indexes, only the media in which they pass. The media does have slightly different refraction indexes for different wavelengths - in that sense you can talk about the refracting index of a media for a ray. In your example the media will have higher refracting index for ray A than for ray B.

 

[MedPR]

I am not completely sure exactly what you're asking here. The rays themselves don't have a refracting indexes, only the media in which they pass. The media does have slightly different refraction indexes for different wavelengths - in that sense you can talk about the refracting index of a media for a ray. In your example the media will have higher refracting index for ray A than for ray B.

After thinking about this overnight, I realized my previous thought process didn't make any sense (well, it did, but it was completely wrong).

Here's what I was thinking, if anyone cares.

In a completely different experiment, you are trying to figure out which has a higher refractive index, water or plastic. So you shoot a light ray from air into water, and an identical light ray also from identical air into plastic. You observe that the light ray bends more towards normal when it refracts in plastic compared to water. Now you know that plastic has a greater refractive index than water.

I was trying to relate that experiment to the one with the prism and two non-identical light rays. I thought that the one that bent more had a lower initial n, compared to the one that didn't bend at all, since they were going through exactly the same media change (air to prism). However, since rays themselves do not have refractive indexes, it's obvious that I was wrong. I also completely forgot about the equation n1lambda1=n2lambda2. If I had remembered that, I would have seen that n1>n2, so lambda1<lambda2.

 

[RiPSTONE]

BUMP. If anyone can give a clearer explanation of this problem that would be awesome!

 

[California Bear]

Also bumping this as well.

Could someone please explain why "the ray that bends more has a higher refractive index"?

 

[steelersfan1243]

Yeah could someone answer this please? Any help would be appreciated, please and thank you.

 

[azor ahai]

light with higher wavelengths experience a lower index of refraction which means higher velocity. this also makes them less easy to be absorbed, bent (refracted), scattered, etc. relative to shorter wavelengths.

it helps to remember that higher wavelengths also experience greater diffraction.

try visualizing the medium as a bunch of annoying particles that get in the way of the light's path. long wavelengths can wrap around these small particles (diffract) and continue along their path while shorter wavelengths end up being scattered.