Answer :
Dm = angle of minimum deviation for the prism when the hollow prism is filled with various liquids.
A = angle of prism.
We assume that the hollow prism with small thickness does not affect. The walls of the glass prism being parallel and of uniform thickness, they do not result in any deviation of the light rays.
If the angle of prism is not small, then the formula is :
[tex]\mu_{Liquid}= Sin (\frac{A+D_m}{2}) / Sin (\frac{A}{2})\\\\Sin(\frac{A+D_m}{2})=\mu_{Liquid}*Sin\frac{A}{2}\\\\A+D_m=2*Sin^{-1}[\mu_{Liquid}*Sin\frac{A}{2}]\\\\D_m=2*Sin^{-1}[\mu_{Liquid}*Sin\frac{A}{2}]-A\\[/tex]
Angle of minimum deviation is proportional to inverse sine of refractive index of the liquid.
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For small angle prism the formula is:
[tex]\mu_{Liquid}= (\frac{A+D_m}{2}) / (\frac{A}{2})=\frac{A+D_m}{A}\\\\D_m=A*(\mu_{Liquid}-1)\\\\D_m\ varies\ directly\ proportional\ to\ Refractive\ index\ of\ liquid.\\[/tex]
The slope of the curve or graph is the angle of minimum deviation (in radians).
A = angle of prism.
We assume that the hollow prism with small thickness does not affect. The walls of the glass prism being parallel and of uniform thickness, they do not result in any deviation of the light rays.
If the angle of prism is not small, then the formula is :
[tex]\mu_{Liquid}= Sin (\frac{A+D_m}{2}) / Sin (\frac{A}{2})\\\\Sin(\frac{A+D_m}{2})=\mu_{Liquid}*Sin\frac{A}{2}\\\\A+D_m=2*Sin^{-1}[\mu_{Liquid}*Sin\frac{A}{2}]\\\\D_m=2*Sin^{-1}[\mu_{Liquid}*Sin\frac{A}{2}]-A\\[/tex]
Angle of minimum deviation is proportional to inverse sine of refractive index of the liquid.
============================
For small angle prism the formula is:
[tex]\mu_{Liquid}= (\frac{A+D_m}{2}) / (\frac{A}{2})=\frac{A+D_m}{A}\\\\D_m=A*(\mu_{Liquid}-1)\\\\D_m\ varies\ directly\ proportional\ to\ Refractive\ index\ of\ liquid.\\[/tex]
The slope of the curve or graph is the angle of minimum deviation (in radians).