Question

derivation of formula for refractive index of a prism with explanation.​

Answer 1

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12th

Physics

Ray Optics and Optical Instruments

Prism

Derive the expression for r...

PHYSICS

Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

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ANSWER

In the given diagram,

OP is the incidence ray, which is making the angle i

1

with normal, and QR is the angle of emergence, which is represented by i

2

. A is the prism angle and μ is the refractive index of the prism.

Now, We know that,

A=Prism angle, δ=Angle of deviation, i

1

=Angle of incidence, i

2

=Angle of emergent.

In the case of minimum deviation,∠r

1

=∠r

2

=∠r

A=∠r

1

+∠r

2

SO, A=∠r+∠r=∠2r

∠r=

2

A

Now, again

A+δ=i

1

+i

2

(∵ In the case of minimum deviation

i

1

=i

2

=i and δ=δ

m

)

So, A+δ

m

=i+i=2i

Now, i=

2

A+δ

m

Now, from snell's rule,

μ=

sin r

sin i

μ=

sin

2

A

sin

2

A+δ

m

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Answer 2

Explanation:

Formula used: Snell's law states that when a light wave passes through the interface of two different media, the ratio of sine of angle of incidence and refraction is a constant. According to the question, minimum deviation is taking place and we know that for minimum deviation, r1=r2=r, i1=i2=i and δ=δm.

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