Question

Sun subtends an angle of ${0.5}^o$ at the pole of a concave mirror of radius of curvature 15 m. The diameter of the image of the sun formed by the mirror is

• A. $8.55cm$
• B. $7.55cm$
• C. $6.55cm$
• D. $5.55cm$

Answer 1

The correct option is C $6.55cm$

$\begin{array}{c}\text{Diameter of image of sun at the focus}\\ \Rightarrow f\theta =\left(\frac{R}{2}\right)\theta \end{array}$

$\begin{array}{cc}\text{Now,}& \frac{R}{2}=\frac{15}{2}=7.5m\\ & =750cm\\ \theta & ={0.5}^{\circ }\times \frac{\pi }{{180}^{\circ }}\\ \theta & =\frac{\pi }{{360}^{\circ }}\end{array}$

$\begin{array}{cc}\text{Diameter}& =\frac{R}{2}\times \theta \\ & =758\times \frac{\pi }{360}\\ & =\frac{75}{36}\times 3.14\\ & =6.55cm\\ \text{Hence,}\left(C\right)\text{is correct option.}& \end{array}$