Question

derive the formula connecting the refractive index of a prism and angle of mean deviation.if the angle of prism is A.​

Answer 1

Answer:

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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