General method of finding deviation by prism.

In the ray diagram shown in figure, find total deviation by prism.

Explanation

Deviation by a prism is given by
`delta=(i_1+i_2)-A`…….(i)
Here,` i_1 =45^@` and `A=75^@`
Therefore, the main objective is to find `i_2` and this angle `i_2` can be obtained under following three
steps.
(i) Applying Snell's law at point M, we have
`mu=(sini_(2))/(sinr_(1))` or `sqrt(2)=sin45^@/sinr_1`
Solving this equation, we get `r_1=30^@`
(ii) `r_1+r_2=A`
`:. 30^@+r_2=75^@`
`:.r_2=45^@`
(iii) Further applying Snell's law at N,
`mu=(sini_(2))/(sinr_(2)) rArr sqrt2=sini_2/sin45^@`
Solving this equation, we get `i_2=90^@`
Now, substituting the value in Eq.(i), we have
`delta=45^@+90^@-75^@`
`=60^@`