A) 1 : 2
B) 1 : 4
C) 1 : 3
D) 1 : 8
Correct Answer: B
Solution :
Angle of deviation \[{{\delta }_{air}}\] is given by when the prism is in air \[{{\delta }_{air}}=(n-1)A=\left( \frac{3}{2}-1 \right)A=\frac{A}{2}\] Again when the prism is immered in water then angle of deviation \[{{\delta }_{water}}\] \[{{\delta }_{water}}=({}_{g}{{n}_{w}}-1)A\] Here \[{}_{g}{{n}_{w}}\] is the refractive index of glass with respect to water so, \[{}_{g}{{n}_{w}}=\frac{{{n}_{g}}}{{{n}_{w}}}=\frac{3\text{/}2}{4\text{/}3}=\frac{9}{8}\] So, \[{{\delta }_{water}}=\left( \frac{9}{8}-1 \right)A=\frac{1}{8}A\] Hence, required ratio is \[\frac{\frac{1}{8}A}{\frac{1}{2}A}=1:4.\]
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