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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Physics
Chapter
Ray Optics

BITSAT 2015 · Physics · Ray Optics

A ray parallel to principal axis is incident at 30^ ^ from normal...

A ray parallel to principal axis is incident at 30∘30^{{}^{\circ}} from normal on concave mirror having radius of curvature RR. The point on principal axis where rays are focussed is QQ such that PQ\mathrm{PQ} is A ray parallel to principal axis is incident at 30^ ^ from normal on concave mirror having radius of curvature R . The

Options

  1. AR2\frac{R}{2}
  2. BR3\frac{R}{\sqrt{3}}
  3. C2R−R2\frac{2 \sqrt{R}-R}{\sqrt{2}}
  4. DR\lleft(1−13)R \l left(1-\frac{1}{\sqrt{3}})

Correct answer

D. R\lleft(1−13)R \l left(1-\frac{1}{\sqrt{3}})

Step-by-step solution

From similar triangles, A ray parallel to principal axis is incident at 30^ ^ from normal on concave mirror having radius of curvature R . The
QCsin⁡30∘=Rsin⁡120∘\frac{Q C}{\sin 30^{{}^{\circ}}}=\frac{R}{\sin 120^{{}^{\circ}}} or QC=R×sin⁡30∘sin⁡120∘=R3\quad Q C=R \times \frac{\sin 30^{{}^{\circ}}}{\sin 120^{{}^{\circ}}}=\frac{R}{\sqrt{3}} Thus PQ=PC−QC=R−R3=R\lleft(1−13)P Q=P C-Q C=R-\frac{R}{\sqrt{3}}=R \l left(1-\frac{1}{\sqrt{3}})
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