[Hunt]

Solve this problem ... if you can!

A plate with parallel faces is an optical medium limited by 2 parallel plane surfaces. It is characterized by its index of refraction n > 1, and thickness e.

If a ray of light strikes one of the surfaces , the 1st incident ray will emerge parallel to the 2nd refracted ray, and the distance ( d ) between the two is called the displacement.

Prove that :

|d| = e Sin (i₁ - r₁) / Cos (r₁)


Hint : i₁ ( 1st angle of incidence ) = r₂ ( 2nd angle of refraction ).?

? ? ? ?? ?i₂ ( 2nd angle of incidence ) = r₁ ( 1st angle of refraction ).

? ? ? ? ? ( These relations can be proven using trigonometry or geometry )

[xiankai]

since the optical medium has an index of refraction n>1, and air has an index of refraction n˜1, the optical medium is denser than air.

by snell's law, sin i₁ / sin r₁ = sin r₂ / sin i₂

hence, i₁ = r₂

and r₁ = i₂

based on the diagram as shown,

x = r₂ - i₂

  = i₁ - r₁

--------------------------------------------------

cos i₂ = e / y

                      y = e / cos i₂

---------------------------------------------------

sin x = d/y

    d = y sin x

      = e sin ( x) / cos i₁

      = e sin (i₁ - r₁) / cos r₁  (proven)

[Hunt]

Very good xiankai , very good indeed.

But let's see how far you can go. Consider this ... a bonus question :

So let's supoose now that there's a real point object A at a certain distance from the plate. The final image of A given by the slab is A^''. Prove that AA^'' = e ( 1 - 1/n ).

[Hunt]

When dealing with light or compound microscopes, one would find this formula interesting after placing a glass slab on a certain specimen, the obj lens would have to be displaced by a distance = AA^'' inorder to re-focus the image.

[teteamigo]

AA''=d / sen i1

d=e * [sen i1 - cos i1 * sen r1/cos r1]


Applying Snell Law,

1*sen i1 = n*sen r1


AA''=e * [ 1 - cos i1/ cos r1 * 1/n ]

For mediums likewise  i1~=r1  , nair~=nplate

Then AA'' is aproximate by AA''=e * (1 - 1/n)

[xiankai]

since someone posted before me, i thought i'll put in a picture of what i was thinking about

the strange thing is, i also got the same solution as teteamigo, but from my diagram its impossible to see that i₁ = r₁ at all 

otherwise the image would be found at where the object is... in otherwords no magnification 

[Donaldson Tan]

Oh mine.. I haven't seen Snell's Law for so long..

I have been indulging myself into chemical science, not optical physics..

[Hunt]

For mediums likewise  i1~=r1  , nair~=nplate

These approximations are invalid here. Try another method.

i1 is by no means equals r1 , makes no sense at all. there would be no refraction then anyway ...

xiankai, you seem to like Geometrical Optics mate.? Bravo!

I have been indulging myself into chemical science, not optical physics..

Well optics is imp for chemistry ,you know. Ofcourse this is very basic but intersting. I think I'll post more difficult problems when I have time.

[xiankai]

thanks, i owe it to you and richard feynman's book on QED

Well optics is imp for chemistry ,you know.

do u mean the stuff involving photons and atoms? how they react and all..

[Hunt]

do u mean the stuff involving photons and atoms? how they react and all..

I'm not sure how much atomic properties of light are used in Chemistry , but it's a sure thing? physical optics is important in analytical chemistry. You may actually know about the application of optics in chemistry a lot more than I do.