JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
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 \(\frac{{15 \times 3}}{{\sqrt 7 }}\,\,cm\)
Answer & Solution
Correct Answer
(D) \(\frac{{15 \times 3}}{{\sqrt 7 }}\,\,cm\)
Step-by-step Solution
Detailed explanation
Given, \(\mu \, = \,\frac{4}{3}\) \(h\,=\,15\,cm\) \(R\,=\,?\) \(\frac{\sin 90^o}{\sin C}=\mu\) \(\Rightarrow \quad \sin C=\frac{1}{\mu}=\frac{R}{\sqrt{R^{2}+h^{2}}}=\frac{3}{4}\) \(\Rightarrow \quad 16 R^{2}=9 R^{2}+9 h^{2}\) or, \({7{R^2} = 9{h^2}}\) or,…
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