Prove that angle of incidence is equal to angle of emergence.

Asked by jgprmr | 15th Jun, 2017, 06:22: PM

Expert Answer:

 
begin mathsize 12px style PQRS space is space the space glass space block.
Let space the space refractive space index space of space air space be space straight n subscript 1 space and space that space of space glass space be space straight n subscript 2.
Ray space AO space is space the space incident space ray space with space angle space of space incidence space as space angle straight i.
OB space is space the space refracted space ray space at space straight O space with space angle space of space refraction space as space angle straight r
This space ray space is space incedent space on space side space RS space of space the space block space at space an space angle space of space incidence space say space angle OBN subscript 1 equals straight r subscript 1
end style
begin mathsize 12px style This space ray space finally space gets space refracted space and space emerges space out space of space the space slab space with space angle space angle straight e.
As space MN space and space straight M subscript 1 straight N subscript 1 space are space normals space to space parallel space surfaces space PQ space and space RS comma space angles space straight r space and space straight r subscript 1 space are space equal space left parenthesis alternate space angles right parenthesis
Consider space refraction space at space straight O colon
sini over sinr equals straight n subscript 2 over straight n subscript 1 space space space space space space space space space space space space space space space space space...... left parenthesis 1 right parenthesis
Similarly comma space consider space reafraction space at space straight B colon
sinr over sine equals straight n subscript 1 over straight n subscript 2 space space space space space space space space space space space space space space space space...... left parenthesis 2 right parenthesis
Multiplying space equations space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma
sini over sinr cross times sinr over sine equals straight n subscript 2 over straight n subscript 1 cross times straight n subscript 1 over straight n subscript 2
therefore sini over sine equals 1
therefore sini equals sine
therefore angle straight i equals angle straight e end style

Answered by Romal Bhansali | 16th Jun, 2017, 11:07: AM