question_answer

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is\[\frac{4}{3},\] and the diver?s eyes are 15 cm below the surface of water. Then the radius of the circle is:

A) \[15\times 3\times \sqrt{5}cm\]              

B) \[15\times 3\sqrt{7}cm\]

C) \[\frac{15\times \sqrt{7}}{3}cm\]                            

D) \[\frac{15\times 3}{\sqrt{7}}cm\]

Correct Answer: D

Solution :

                Given,\[\mu =\frac{4}{3}\] h = 15 cm R = ? \[\frac{\sin {{90}^{o}}}{\sin C}=\mu \]\[\Rightarrow \]\[\sin C=\frac{1}{\mu }=\frac{R}{\sqrt{{{R}^{2}}+{{h}^{2}}}}=\frac{3}{4}\] \[\Rightarrow \]\[16{{R}^{2}}=9{{R}^{2}}+9{{h}^{2}}\]or,\[7{{R}^{2}}=9{{h}^{2}}\] or\[R=\frac{3}{\sqrt{7}}h=\frac{3}{\sqrt{7}}\times 15cm\]