Does the prism equation (i+e = A+δ) apply to all prisms?

[Fiona Rozario]

TL;DR Summary

Does prism equation apply to all prims? And does it fail for normal incidence on a prism?

Does prism equation (i+e = A+δ) apply to all prims, equilateral and right angled? And does it fail for normal incidence on a prism?
For eg. when light is incident normally on one of the sides of an equilateral prism, it deviates the light through 60°. i+e = 0. A+δ = 60+60 = 120°.

 

[sophiecentaur]

Can you be a bit more specific about this? It may be obvious to you but what actual Prism Equation are you referring to and what are A and δ (dispersion?)?. A diagram or a reference always helps.

 

[Fiona Rozario]

Can you be a bit more specific about this? It may be obvious to you but what actual Prism Equation are you referring to and what are A and δ (dispersion?)?. A diagram or a reference always helps.

Prism equation - i+e = A+δ, where, i is angle of incidence, e is angle of emergence, A is angle of the prism and δ is angle of deviation. The case of normal incidence that I am referring is to, is as in the diagram.

 

[sophiecentaur]

Thanks. Well - this is just a bit of geometry which describes a case of light going through a prism where there is never any refractive change of angle (it's all normal incidence and TIR). The prism where this is used most is a right angled 45 degree prism which I am sure you have seen.

The example you quote of a 60 degree prism also happens to 'work' if you make that apex angle wider, the ray hits lower and lower down side AC. It then hits side BC,and the angle C has to be bigger and bigger so that the exiting ray strikes BC normally. Right angled and equilateral prisms are 'compact' compared with other possible prisms that will act as 'good mirrors'.

It's a special case of a special case and it's not something I have come across before. The writer of the book must have found it interesting but it seems to have confused you. I still don't get your terminology "i and e"? and you call it "the prism equation" but I think it is just one of all the possible equations.

 

[hutchphd]

Summary:: Does prism equation apply to all prims? And does it fail for normal incidence on a prism?

Does prism equation (i+e = A+δ) apply to all prims, equilateral and right angled? And does it fail for normal incidence on a prism?

As mentioned by @sophiecentaur there are many different "prism equations". I believe the equation you quote is not appropriate for paths that contain total internal reflections, but will work for any wedge prism

 

[sophiecentaur]

As mentioned by @sophiecentaur there are many different "prism equations". I believe the equation you quote is not appropriate for paths that contain total internal reflections, but will work for any wedge prism

@Fiona Rozario Absolutely your OP didn't quote the context. You have to realize that this could be read by bears with very little brain. To access what they know, you need to press the right buttons. Surplus information in an OP costs nothing and can get quick results.

So you are looking for a relationship in a special class of prisms in which the entry and exit faces are appropriate for normal rays and in which the third face is suitable for TIR. I think I can confirm that your equation will apply to any prism that follows those requirements. Try drawing some on paper (as I would do) and you will see what I mean - or do some trig, perhaps and you may get an equation that tells you permitted values.

What is the title of that book? Is it general optics or some specialist optical equipment?

 

[Hamiltonian]

What is the title of that book? Is it general optics or some specialist optical equipment?

that's from a high school(10th grade) textbook called Concise physics by Selina its followed in many Indian schools

 

[Hamiltonian]

Summary:: Does prism equation apply to all prims? And does it fail for normal incidence on a prism?

Does prism equation (i+e = A+δ) apply to all prims, equilateral and right angled? And does it fail for normal incidence on a prism?
For eg. when light is incident normally on one of the sides of an equilateral prism, it deviates the light through 60°. i+e = 0. A+δ = 60+60 = 120°.

the "prism equation" you are talking about is simply plain geometry and nothing more and hence applies to all prisms. (go through its derivation again)

Prism equation - i+e = A+δ, where, i is angle of incidence, e is angle of emergence, A is angle of the prism and δ is angle of deviation. The case of normal incidence that I am referring is to, is as in the diagram.

look at the diagram carefully i = 90, e = 90. and A+δ = 180 which is clearly satisfying the "prism equation"

 

[sophiecentaur]

plain geometry

Exactly. There is no refraction involved so you can forget the Physics of Snell's Law. It is hard for students to understand the context of some of the questions that they find in textbooks. This particular question will just have been presented 'bare bones' and the risk is that the student will try to see some special Physical Significance in it. The question should have had an initial sentence stating that prisms can be used as good reflectors as long as the angles are chosen so as to avoid dispersion. The OP uses the term "prism equation" which implies that it's THE prism equation - but it is not particularly significant at all. There are much more important 'equations' about prisms that tell you about the dispersion angle and the reason for choosing a particular prism angle in a spectrometer.

 

[shiv409]

Prism equation - i+e = A+δ, where, i is angle of incidence, e is angle of emergence, A is angle of the prism and δ is angle of deviation. The case of normal incidence that I am referring is to, is as in the diagram.View attachment 266986

Can you please tell me which book is this?

 

[shiv409]

Can you please tell me which book is this?

The book from where you attached the diagram.

 

[sophiecentaur]

This is an ancient thread so it's unlikely we can help the OP - unless he / she has responded recently.