A ray parallel to principal axis is incident at \[30{}^\circ \] from normal on concave mirror having radius of curvature R. The point on principal axis where rays are focussed is \[Q\]such that PQ is |
A) \[\frac{R}{2}\]
B) \[\frac{R}{\sqrt{3}}\]
C) \[\frac{2\sqrt{R}-R}{\sqrt{2}}\]
D) \[R\left( 1-\frac{1}{\sqrt{3}} \right)\]
Correct Answer: D
Solution :
From similar triangles, |
\[\frac{QC}{\sin 30{}^\circ }=\frac{R}{\sin 120{}^\circ }\] Or \[QC=R\times \frac{\sin 30{}^\circ }{\sin 120{}^\circ }\] |
\[=\frac{R}{\sqrt{3}}\] |
Thus \[PQ=PC-QC\] |
\[=R-\frac{R}{\sqrt{3}}\] |
\[=R\left( 1-\frac{1}{\sqrt{3}} \right)\] |
You need to login to perform this action.
You will be redirected in
3 sec