Explain about relation between refractive index and angle of minmum deviation

As a ray of light enters any medium, the ray's direction is deflected, based on the entrance angle (typically measured relative to the surface normal), the material's refractive index, and according to Snell's law. A beam passing through an object like a prism or water drop is deflected twice: once entering, and again when exiting. The sum of these two deflections is called the deviation angle.
The deviation angle in a prism depends upon:

1. Refractive index of the prism
2. Angle of prism
3. Angle of Incidence
   
   Let, A be apex angle and $\delta$_m is minimum deviation 

We know , at $\delta$_m , i = e and r₁=r₂=r (say)

Now, 
A =  r₁+ r₂  

A = 2r

r = $\frac{A}{2}$
Also, I +e= A +$\delta$
2i = A+ $\delta$_m 

i = $\frac{a+\delta _{m} }{2}$

$\mu$ = $\frac{sin\frac{A+\delta _{m}}{2}}{sin\frac{A}{2}}$

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Updated on: 10-Oct-2022

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