Question

In the given figure, a ray of light $1\text{cm}$ above the principal axis get reflected from a concave mirror and intersect the principal axis at $Y$. Find the length $PY$ if the radius of curvature of the mirror is $2\text{cm}$.

• A. $(\sqrt{3}-1)\text{cm}$
• B. $2(1-\frac{1}{\sqrt{3}})\text{cm}$
• C. $(1-\frac{1}{\sqrt{3}})\text{cm}$
• D. $\sqrt{3}\text{cm}$

Answer 1

The correct option is B $2(1-\frac{1}{\sqrt{3}})\text{cm}$


In $△ABC$,
$\sin \theta =\frac{BC}{AC}$
$\Rightarrow \sin \theta =\frac{1}{2}[AC=R=2\text{cm}]$
$\Rightarrow \theta ={30}^{\circ }$
Now, focal length, $PY=R-\frac{R}{2}\sec \theta$
$\Rightarrow PY=R-\frac{R}{2}\sec {30}^{\circ }$
$\Rightarrow PY=2-\frac{2}{2}.\frac{2}{\sqrt{3}}$
$\Rightarrow PY=2(1-\frac{1}{\sqrt{3}})\text{cm}$