Refraction/Snell's Equation Question

[rocketbooster]

A little confused on refraction...

How does angle of incidence relate to angle of refraction in all circumstances?

n1sin(incidentangle)=n2sin(refractiveangle)


For n1<n2 -
Assuming you don't change the indeces of refraction, if you increase the incident angle, the level of refraction increases, right? Since n1<n2, this means it refracts more in the direction towards the normal line (the vertical line). Since the refractive angle is measured from the normal line, doesn't the refractive angle decrease then?

I'm just confused because of this TBR problem. It shows white light going through a prism. It says if you increase the angle of incidence, then the colors are dispersive based on there being more refaction and a greater angle of refraction. The part I don't understand is how the angle of refraction is greater. Shouldn't the refractive angle be smaller since it's refracting more in the direction of the normal, which is where this angle is measured from? If n1>n2, then I understand why more refraction means a greater refractive angle. In that case, the refractive angle is greater than 45 because it is refracts more towards the horizontal line (line between the 2 media).

The answer solution just says "remember bigger incident angle means bigger refractive angle." I can only see this being true if n1>n2. For n1<n2, shouldn't it be bigger incident angle means smaller refractive angle? The problem deals with white light from air into a prism. The n of prism should be > n of air, thus n2>n1. Is this just a typo in the book? I got the correct answer correctly, but the explanation to the answer solution is confusing the hell out of me.

Argh, can someone help me out? Thanks.

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[0Complications]

I'm not sure about about all the parts of question, but the angle of refraction is essentially the same as the angle of incidence, so if you increase the angle of incidence you then have to increase the angle of refraction (depending on your medium).

Also, you talked about increasing the angle of incidence and having the angle of refraction move closer to the normal line, this only happens if the medium has a lower refractive index than the medium of incidence. Since in your example the medium of refraction is a crystal and the incidence angle is in air, the angle of refraction should get larger and move further away from the normal line.

 

[rocketbooster]

I'm not sure about about all the parts of question, but the angle of refraction is essentially the same as the angle of incidence, so if you increase the angle of incidence you then have to increase the angle of refraction (depending on your medium).

Also, you talked about increasing the angle of incidence and having the angle of refraction move closer to the normal line, this only happens if the medium has a lower refractive index than the medium of incidence. Since in your example the medium of refraction is a crystal and the incidence angle is in air, the angle of refraction should get larger and move further away from the normal line.

If the refractive angle is getting further from the normal line, that would imply there is less refraction, though. The level of refraction is based on how far is refracts from the imaginary line if the light ray from the incident angle had gone straight through the prism (which would only be straight if the media had equal n values), right? If you increase that refractive angle, you are getting closer to the imaginary, straight line. Until this angle passes that imaginary line and begins move past the 45 degree mark and up toward the horizontal line between the medium, the increasing angle is causing less refraction. Once it passes that 45 degree mark and moves up, counter-clockwise toward that horizontal, then refraction of the light is increasing. Doesn't that make sense? Because from that imaginary straight line from the incident ray, increased refraction could go clockwise, which decreases the refractive angle, or go counter-clockwise, which increases the refractive angle. If it were to go counter-clockwise enough, the refractive angle would hit 90 degrees and be total internal reflection and thus no refraction at all. Is that right?

I'm just confused as to what defines the ray being refracted more. Can you explain that to me? Any increasing change in either direction from that straight dotted line from the incident ray straight through the more refractive glass/crystal means positive refraction from my understanding. I think that's what's confusing me. Help?

 

[0Complications]

I think your confusion is coming from your normal line. The normal line does not follow the incident ray, but rather is perpendicular to the medium. I created an example below.

The vertical line is the normal line, the horizontal line is the medium, and the angled lines my rays of incidence/refraction, and the red dots represent the angle of incidence and the blue dots represent the angle of refraction.

The angles are measured FROM the NORMAL LINE, so imagine that my incident ray which is obviously going from one medium to another with the same refractive index (sorry, limitation on my keyboard 🙂). Now imagine the incident and refractory rays are connected, say like a stick (for an analogy), now if you push down on the incident ray moving it closer to the medium, the incident ray AND the refractive ray moves away from the normal line ON BOTH SIDES, because remember with our example they are both connected. This means the refractive line moves closer to the medium surface (and yes, you are right, when the angle gets to 90 degrees you can get total internal reflection).

\...|
.\..|
..\.|
...\|
-------------------------------------
....|\
....|.\
....|..\
....|...\

I hope this helps.

 

[rocketbooster]

I think your confusion is coming from your normal line. The normal line does not follow the incident ray, but rather is perpendicular to the medium. I created an example below.

The vertical line is the normal line, the horizontal line is the medium, and the angled lines my rays of incidence/refraction, and the red dots represent the angle of incidence and the blue dots represent the angle of refraction.

The angles are measured FROM the NORMAL LINE, so imagine that my incident ray which is obviously going from one medium to another with the same refractive index (sorry, limitation on my keyboard 🙂). Now imagine the incident and refractory rays are connected, say like a stick (for an analogy), now if you push down on the incident ray moving it closer to the medium, the incident ray AND the refractive ray moves away from the normal line ON BOTH SIDES, because remember with our example they are both connected. This means the refractive line moves closer to the medium surface (and yes, you are right, when the angle gets to 90 degrees you can get total internal reflection).

\...|
.\..|
..\.|
...\|
-------------------------------------
....|\
....|.\
....|..\
....|...\

I hope this helps.

Yeah, your pic is perfect. Now, can you explain how the stick moves when you increase the level of REFRACTION, not the refractive angle? If the stick moves down or up, it is deviating from its initial position either way. So isn't any deviation away from its original position (in the CW or CCW direction) considered that the ray is refracting more than before?

 

[0Complications]

Yeah, your pic is perfect. Now, can you explain how the stick moves when you increase the level of REFRACTION, not the refractive angle? If the stick moves down or up, it is deviating from its initial position either way. So isn't any deviation away from its original position (in the CW or CCW direction) considered that the ray is refracting more than before?

I think I see what you're saying. So, now if you imagine the lower part of the 'stick' (ray of refraction) on a hinge (I put it on a hinge to denote that the incident ray is not changing when you shift the refractive ray) then the way the ray deviates is dependent on the medium. So if the medium has a higher refractive index then it will increase the refraction of the ray, by moving it closer to the medium border or to the right (remember it's on a hinge, so to the right will swing it like a pendulum attached at the point it meets the medium). This shift occurs simply by increasing the refractive index of the medium the incident ray of light is moving into. Moving the stick to the right will move it FURTHER away from the NORMAL line causing the angle of refraction to INCREASE. So essentially increasing the level of refraction does increase the refractive angle unless the level of refraction (refractive index) is increased in both mediums.

Now let's say the refractive ray is in a medium with a LOWER RI than than the incident ray, now the 'stick' will move to the LEFT causing the angle of refraction to decrease. I suppose you could thing of this as a (-) shift.

I would agree that this is still an increase in the refraction from the perspective of a ray of light from an RI of 1 into a medium of 1 (or whatever value just insuring that the mediums are the same). I think anytime you deviate from the incident ray you're getting an increase in RI in one medium or the other, but your angle is definitely not increasing, it is decreasing in this example to the left.

That's the best I've got for you, man. My physics isn't my strongest suit, so maybe someone else can chime in to explain more specifically some interactions. Although, I can tell you I've never missed an AAMC refraction question and I ALWAYS use this logic when solving them. I've never busted out a formula for it, I just ask myself which medium's RI is greater then I ask myself, will that move the i or r ray closer or further away from the normal line then I ask if it's an increasing or decreasing the angle of r or i and presto. I guess, technically I use the formula, but I never think about it that way. I just conceptualize the idea.

Good luck, man.

 

[rocketbooster]

I think I see what you're saying. So, now if you imagine the lower part of the 'stick' (ray of refraction) on a hinge (I put it on a hinge to denote that the incident ray is not changing when you shift the refractive ray) then the way the ray deviates is dependent on the medium. So if the medium has a higher refractive index then it will increase the refraction of the ray, by moving it closer to the medium border or to the right (remember it's on a hinge, so to the right will swing it like a pendulum attached at the point it meets the medium). This shift occurs simply by increasing the refractive index of the medium the incident ray of light is moving into. Moving the stick to the right will move it FURTHER away from the NORMAL line causing the angle of refraction to INCREASE. So essentially increasing the level of refraction does increase the refractive angle unless the level of refraction (refractive index) is increased in both mediums.

Now let's say the refractive ray is in a medium with a LOWER RI than than the incident ray, now the 'stick' will move to the LEFT causing the angle of refraction to decrease. I suppose you could thing of this as a (-) shift.

I would agree that this is still an increase in the refraction from the perspective of a ray of light from an RI of 1 into a medium of 1 (or whatever value just insuring that the mediums are the same). I think anytime you deviate from the incident ray you're getting an increase in RI in one medium or the other, but your angle is definitely not increasing, it is decreasing in this example to the left.

That's the best I've got for you, man. My physics isn't my strongest suit, so maybe someone else can chime in to explain more specifically some interactions. Although, I can tell you I've never missed an AAMC refraction question and I ALWAYS use this logic when solving them. I've never busted out a formula for it, I just ask myself which medium's RI is greater then I ask myself, will that move the i or r ray closer or further away from the normal line then I ask if it's an increasing or decreasing the angle of r or i and presto. I guess, technically I use the formula, but I never think about it that way. I just conceptualize the idea.

Good luck, man.

yes, yes, yes! you understand EXACTLY what I am saying.

I think you reversed your directions, though. think of total internal reflection. it's when the ray goes from higher RI to lower RI, right? the medium with the refractive ray has lower RI, and in TIR the "stick" moves right toward the horizontal. it's when the stick reaches that horizontal line that TIR occurs and thus no more refraction. that would mean the refractive ray in less RI means "stick" moves right. consequently, when the refractive ray is in higher RI, the "stick" moves to the left.

am I correct? or am I the one who reversed it?

 

[0Complications]

yes, yes, yes! you understand EXACTLY what I am saying.

I think you reversed your directions, though. think of total internal reflection. it's when the ray goes from higher RI to lower RI, right? the medium with the refractive ray has lower RI, and in TIR the "stick" moves right toward the horizontal. it's when the stick reaches that horizontal line that TIR occurs and thus no more refraction. that would mean the refractive ray in less RI means "stick" moves right. consequently, when the refractive ray is in higher RI, the "stick" moves to the left.

am I correct? or am I the one who reversed it?

Nope. You are right. The 'stick' would move towards the normal line (left) if it were in a medium with a higher RI than the incident 'stick'. Good catch!