Question

Define angle of prism and derive an expression for angle of prism in terms of refracting angle i.e. A = r1 + r2
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Answer 1

Answer:

•In the given diagram,

•In the given diagram,OP is the incidence ray, which is making the angle i

•In the given diagram,OP is the incidence ray, which is making the angle i 1

•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

•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

•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.

•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,

•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

•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 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

•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

=∠r 1 +∠r 2

=∠r 1 +∠r 2 SO, A=∠r+∠r=∠2r

=∠r 1 +∠r 2 SO, A=∠r+∠r=∠2r∠r= 2A_Now, again

Now, againA+δ=i 1 +i 2 (∵ In the case of minimum deviation

Now, againA+δ=i 1 +i 2 (∵ In the case of minimum deviation i 1 =i 2 =i and δ=δ m )So, A+δ

Now, againA+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=2iNow, i= 2A+δ mNow, from snell's rule,

Now, from snell's rule,μ= sin rsin i_μ= sin 2A sin 2A+δ m