Refraction Through Prism Assignment Help

Optical Physics - Refraction Through Prism

Refraction Through Prism

A ray of light suffers two refraction, on passing through a prism and hence deviates through a certain angle from its original path.

(a) Calculation of angle of deviation

In fig. ABC is principle section of a prism with angle of prism = A

A ray of light KL is incident on the face AB of the prism at ∠i1. It bends towards the normal N1O and is refracted along LM at ∠i1. The refracted ray LM is incident at ∠r2 on face AC of the prism. It bends away from normal N2O and emerges along MN at ∠i2. In passing through the prism, ray KL suffers two refractions and has turned through an ∠QPN = δ, which is the angle of deviation.

In Δ PLM,  δ  = ∠PLM + ∠PML

δ  = (i1 – r1) + (i2 – r2)

δ  = (i1 + i2) – (r1 + r2)                                                             (1)

In OLM, ∠O + r1 + r2 = 180°                                                   (2)

In quadrilateral ALOM,

As L + M = 180° (? each angle is 90°)

A + ∠O = 180° (? sum of four angles of a quad. = 360°)

Using eqn. (2), 

∠O + r1 + r2 = A + ∠O

r1 + r2 = A                                                                              (3)

put in (1),  δ  = (i1 + i2) – A                                                    (4)

If  µ  is refractive index of the material of the prism, then according to Snell’s law,

µ  = sin i1/sin r1 = i1/r1 (when angles are small)

∴  i1 =  µ r1; similarly, i2 =   µ r2

Putting in (4), we get

δ  = ( µ r1 +  µ r2) – A 

δ  =  µ  (r1 + r2) – A 

Using (3), we obtain,

δ  = µA – A                                                                               (5)

This is the angle through which a ray deviates on passing through a thin prism of small refracting angle A. - Physics HelpOptical Physics Assignments, Refraction Through Prism Assignment Help, Refraction Through Prism Homework Help, Refraction Through Prism Assignment Tutors, Refraction Through Prism Solutions, Refraction Through Prism Answers, Optical Physics Assignment Tutors

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