Diagram:
Given : r1=30° and r2=45° ,μ1=1
To find : μ2
Formula : Snell's law →μ1sini=μ2sinr
Solution : As ∆SAB is right angled triangle,
\(\therefore\) i1+i2= 90°
According to snell's law ,
For refraction at A,
sini1=μ2sin30°
\(\therefore \) sini1=μ2(1/2) .......(1)
For refraction at B ,
sini2=μ2sin45°
\(\therefore\) sini2=μ2(1/√2)
\(\therefore\) sin(90°-i1)=cosi1=μ2(1/√2) ...(2)
Square and add (1) and (2)
\(\therefore\) sin²i1+cos²i2=1=(μ2)²(3/4)
\(\implies \,\mu _\textbf2=\frac{\textbf2}{\sqrt{\textbf3}}\)
Refractive index of liquid is \(\frac{\textbf2}{\sqrt{\textbf3}}\)