Prism equation OR Prism formula OR Refraction through prism—
In a prism there are two refracted surface AB and AC.
Case-I—When a ray of light passes from rare to denser medium it bends towards the normal.
Case-II—When a ray of light passes from denser to rarer medium it bends away from the normal.
![](https://www.sarthaks.com/?qa=blob&qa_blobid=8217370097393433250)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=17001787938677437750)
In quadiralateral ALKP :—
![](https://www.sarthaks.com/?qa=blob&qa_blobid=4623323183585391665)
Eqn (8) is called 1st eqn of prism. Hence angle of prism is the sum total of angle of refraction through both the surface.
Using eqn (8) in (4)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=5777972642994459388)
Eqn (9) is called 2nd eqn of prism. It starts that the sum total of angle of incidence & angle of emergence is equal to sum angle of deviation and angle of prism.
Case-III Minimum deviation produced by a prism—
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13093869834207185047)
Deviation produced by a prism is the angle b/w extended line of incident ray and emergent ray. For minm deviation produced by prism,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12701574643904955907)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10707606045922821443)
A/C to prism's second relation
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10500805353840972910)
A/C to snell's law,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=4852677205613077745)
Eqn (9) is the general expression for minimum deviation produced by a prism.