Question

prism formula derivation ☺___!!!!

Answer 1

PRISM FORMULA :-

The figure below shows the passage of light through a triangular prism ABC.



The angles of incidence and refraction at first face AB areiandr1.

The angle of incidence at the second face AC isr2and the angle of emergencee.

δis the angle between the emergent ray RS and incident ray PQ and is called the angle of deviation.

Here, PQN =i



RQO =r1

QRO =r2

KTS = δ

TQO =iand RQO =r1, we have

TQR =i r1

TRO =eand QRO =r2

TRQ =er2

In triangle TQR, the side QT has been produced outwards. Therefore, the exterior angleδshould be equal to the sum of the interior opposite angles.

i.e, δ= TQR + TRQ = (i r1) + (er2)

δ= (i+e) (r1+r2) (i)

In triangle QRO,

r1+r2+ ROQ = 180 (ii)

From quadrilateral AROQ, we have the sum of angles (AQO + ARO = 180). This means that the sum of the remaining two angles should be 180.

i.e , A + QOR = 180 [A is called the angle of prism]

From equations (i) and (ii),

r1+r2= A (iii)

Substituting (iii) in (i), we obtain

δ= (i+e) A



Answer 2

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