Question

The sun (diameter $d$) subtends an angle $\theta$ radians at the pole of a concave mirror of focal length $f$. What is the diameter of the image of the sun formed by the mirror ?

• A. $\theta f$
• B. $2\theta f$
• C. Zero
• D. $\infty$

Answer 1

The correct option is A $\theta f$


Since the sun is very distant, the distance between mirror and the sun $\left(u\right)$ is very large and so $\left(\frac{1}{u}\right)$ is practically zero.
So $\frac{1}{v}+0=\frac{1}{-f}$
i.e., $v=-f$
i.e., the image of sun will be formed at the focus and will be real, inverted and diminished.
Now as the rays from the sun subtend an angle $\theta$ radians at the pole, then in accordance with Fig.
$\theta =\frac{A^{{}^{\prime }}{B}^{{}^{\prime }}}{FP}=\frac{d}{f}$
[where $d$ is the diameter of the image of the sun.]
i.e., $d=\theta f$
Hence, option (a) is correct.

$\begin{array}{c}\text{Why this question?}\\ \text{Light coming from a very distant point can be considered parallel hence}\\ \text{after reflection will pass through the focus of the spherical mirror.}\end{array}$