Question

The sun (diameter $D$ ) subtends an angle $\theta$ radian at the pole of a concave mirror of focal length $f$ . The diameter of the image of the sun formed by the mirror is:

• A. $f\theta$
• B. $2f\theta$
• C. $\frac{2f\theta }{D}$
• D. $D\theta$

Answer 1

Answer: (A)

Clearly Image distance is $v=f$
$tan\left(\frac{\theta }{2}\right)=\frac{A^{\prime }F}{PF}=\frac{A^{\prime }F}{f}{A}^{\prime }F=f(tan\left(\frac{\theta }{2})\right)A^{\prime }F=f(\frac{\theta }{2})A^{\prime }{B}^{\prime }=2A^{\prime }F=f(\theta )$