Answer to Question #96919 in Optics for Halima

Question #96919
Two thin(small angled)prism are combined to produce dispersion without deviation. One prism has angle 5A^° and refractive index 1.56.if the other prism has refractive index 1.7,what is its angle?
1
Expert's answer
2019-10-22T10:17:06-0400

Angle of Prism


We need to find the Angle of the second prism


Solution:


We know the formula to find the deviation produced by a Prism, that is



d=(μ1)Ad = (\mu - 1) A

In this,


d = Deviation produced by the Prism


μ=\mu = Refractive index of the Prism


A = Angle of the Prism


Here, We are working on two prisms.


d1=d_1 = Deviation produced by the first Prism


d2=d_2 = Deviation produced by the second Prism


A1=A_1 = Angle of the first Prism = 5o5^{o}


A2=A_2 = Angle of the second Prism


μ1=\mu_1 =  Refractive index of the first Prism = 1.56


μ2=\mu_2 = Refractive index of the second  Prism = 1.7


Without deviation, means,

d1=d2=0d_1 = d_2 = 0

Th equations

d1=(μ11)A1d_1 = (\mu_1 - 1) A_1


d2=(μ21)A2d_2 = (\mu_2 - 1) A_2


(μ11)A1=(μ21)A2(\mu_1 - 1) A_1 =(\mu_2 - 1) A_2

PLug the values in this,

(1.561)5=(1.71)A2(1.56 - 1) 5 = (1.7 - 1) A_2



A2=0.56×50.7=4oA_2 = \frac {0.56 \times 5} {0.7} = 4^{o}

Answer: Angle of the second Prism

A2=4oA_2 = 4^{o}


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