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  • (a) Plot a graph for angle of deviation as a function of angle of incidence for a triangular prism. (b) Derive the relation for the refractive index of the prism in terms of the angle of minimum deviation and angle of prism.

(a) Plot a graph for angle of deviation as a function of angle of incidence for a triangular prism.

(b) Derive the relation for the refractive index of the prism in terms of the angle of minimum deviation and angle of prism.

 

 

 
 
 
 
 

Answers (1)

(a) A graph for the angle of deviation as a function of angle of incidence for a triangular prism;

       

(b) We know that,

n_{21}=\frac{\sin i}{\sin r}

From the figure,

Consider the quadrilateral AQNP

\\<APN=<AQN=90\\<A+<QNP=180..........(1)\\<QNP=180-(r_1+r_2)\text{from triangle QPN}\\<QNP+(r_1+r_2)=180...........(2)\\\text{from(1) and(2)}\\r_1+r_2=A

At minimum deviation i.e, \delta =\delta m, i=e and r_{1}=r_{2}=r

     \therefore r=\frac{A}{2} _______(i)

From the figure, we have 

\delta =(i-r_{1})+(e-r_{2})

\therefore \delta m =(i+e)+(r_{1}+r_{2})

i=\frac{A+\delta m}{2}_______(ii)

From eqn. (1) and (2) , we have,

n_{21}=\frac{\sin i}{\sin r}=\frac{sin\frac{A+\delta m}{2}}{\sin \frac{A}{2}}

Posted by

Safeer PP

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