Question

A prism is made of glass of refractive index 1.5. If the angle of minimum deviation is equal to the refracting angle of the prism, calculate the angle of the prism.

Answer 1

Given, `mu=1.5 ` and `A=delta_(m i n)`
At minimum deviation,
`r=A//2` and `delta_(min)=2i-A`
Substituting for A, we get `i=delta_(min)`
But `mu=(sin ((delta_(m)+A)/(2)))/(sin((A)/(2)))=(sinA)/(sin[(A)/(2)])=2cos[(A)/(2)]`
Therefor, `1.5=2cos[(A)/(2)]` or `A =cos^(-1)((3)/(4))`