WBJEE · Physics · Ray Optics
The cross-section of a reflecting surface is represented by the equation \(x^{2}+y^{2}=R^{2}\) as shown in the figure. A ray travelling in the positive \(x\) direction is directed toward positive y direction after reflection from the surface at point \(M\). The coordinate of the point \(\mathrm{M}\) on the reflecting surface is
- A \(\left(\frac{\mathrm{R}}{\sqrt{2}}, \frac{\mathrm{R}}{\sqrt{2}}\right)\)
- B \(\left(-\frac{\mathrm{R}}{2},-\frac{\mathrm{R}}{2}\right)\)
- C \(\left(-\frac{R}{\sqrt{2}}, \frac{R}{\sqrt{2}}\right)\)
- D \(\left(\frac{R}{\sqrt{2}},-\frac{R}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-\frac{R}{\sqrt{2}}, \frac{R}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
\(x^{2}+y^{2}=R^{2}\) \(2 x+2 y \frac{d y}{d x}=0\) \(\frac{d y}{d x}=-\frac{x}{y}=\tan 45^{\circ}=1\) \(\therefore x=-\frac{R}{\sqrt{2}}\) \(y=+\frac{R}{\sqrt{2}}\)
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