Solving Ray Optics Problem: Understanding Refraction and Deviation

[thunderhadron]

Hi friends,
Please help me in answering this problem

The problem is as follows,

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/s480x480/557923_2937818221818_1718139220_n.jpg

Well,

As far as I am concerned, When white light fall on the first surface, after refraction through it, the ray will be deviated. But the glass material will have different refractive indexes for the seven colors (VIBGYOR)of light. Hence they will deviate at different angles of deviations. And Violet will be at the lowest position on the screen.

And after the second refraction from the second surface, all the rays will go parallel to the initial light ray again.
Hence after the two refractions the light will split into seven colors. And the ray diagram would be like this -

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn1/s480x480/11334_2937788181067_1369934100_n.jpg


Hence the answer should be option (C)

But book says answers of the question are option (B) & (C).

Please friends help me in solving this problem.

Thanks to all in advance.

 

[Simon Bridge]

To get the emergent beam to be colored, you need opposites sides at an angle to each other. See "prism".
For the effect you are talking about to be so big would be pretty unusual - when you look through a window, you don't normally see a rainbow halo around the things you see do you?

 

[thunderhadron]

Yes Simon, like prisms, I also consider them inside the glass slab to get the answer. But that is not my motto. Motto is to know the actual truth. When watching from outside the window we never see rainbow type picture. But as I said according to all the theories I have read in books, the ray should deviate into colors. Why it is not happening?

 

[thunderhadron]

To get the answer same like what is given in the question we have to divide the the slab into a set of two prisms. And the figure would be like

https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-snc7/s480x480/312402_2940623131939_1714481763_n.jpg

But here we have divided the slab into two prisms and a boundary inside it. How can we decided a separating boundary inside a slab in any random way. It is not satisfying me.

 

[Simon Bridge]

It is not satisfying me.

1. prisms don't work like that - you can't recombine the colors.
2. correct answers don't have to satisfy you
3. the suggestion is, in fact, wrong - to get refraction in the middle you'd have to have a change in refractive index there.

The kinds of glass normally available will not separate different wavelengths by a big enough angle to get a spectrum - so white light in gets you white light out for answer B.

However, just because the angle does not diverge does not mean the different components don't separate out ... inside the glass, they travel at different speeds along the ray.

To gain a better understanding - draw in the whole wavefronts for a wider beam instead of just one ray.

 

[thunderhadron]

to get refraction in the middle you'd have to have a change in refractive index there.

.

Exactly simon, We can't make such a ray diagram for this. I was just trying to match the given answer, which I am thinking wrong.

 

[thunderhadron]

To gain a better understanding - draw in the whole wavefronts for a wider beam instead of just one ray.

That means ray optics can't give the correct answer of this question?

Shall we move towards wave optics?

Are you ok with the given answers according to question?

 

[Simon Bridge]

That means ray optics can't give the correct answer of this question?

Ray optics, by itself, is not a complete description for light ... it does not handle the compression of the wavelengths in a refractive material for example.

Shall we move towards wave optics?

You have to use the model that works for the situation.
There will come a point where you will need quantum mechanics... which manages to include both the wave and the ray optics.

Are you ok with the given answers according to question?

Yes - depending on the context established by the course-material being tested (which I don't know).

Also see:
https://www.physicsforums.com/showthread.php?t=61818

I should add that the different colors will refract to a different angle at the air-glass incident interface, but the different colors would be parallel when they exit. The effect is very small so you won't notice.

I do think the answer is a bit fussy though. It does specify that the beam is narrow - a very narrow beam should show a bit of dispersion around the edges after it has exited the block. I would not have set the test that way ... they key is in how the course was taught.

 

[jlefevre76]

After traveling through the glass (or whatever), the rays all leave going the same direction. They DO split a bit, but not enough to be noticeable, especially if the slab is small (thin). For a prism, however, the rays LEAVE the prism going in different directions, so the small angles can be seen at a distance. Notice with a prism, if you shine the light through at an object very close to the prism, the light still appears pretty much white (unless the prism is really thick in the direction of the light). As you move the object further away from the prism, the light separates even more.

I hope that helps conceptually a little bit. If it's any consolation, I don't like the original homework/test question very much, as the answers are contradictory. Answer "B)" would be more correct if they had said something about the beam APPEARS white.

 

[Emilyjoint]

The emerging rays are parallel because the sides of the block are parallel.
There is no divergence between different wavelengths.