Question

Sun subtends an angle $\theta$ radians at pole of a concave mirror of radius of curvature $R$. If distance of image of sun from pole of the mirror is $d$ and area of the image of the sun is $A$ then choose the correct option(s).

• A. Value of $A$ is $\frac{\pi R^2 \theta^2}{4}$
• B. Value of $A$ is $\frac{\pi R^2 \theta^2}{16}$
• C. Value of $d$ is $\frac{R}{2}$
• D. Value of $d$ is $\frac{R}{4}$

Answer 1

Answer: (B), (C)

B, C

Answer 2

The sun is at infinity, so its image forms at the focal plane. The focal length of the concave mirror is $f = R/2$. Thus, the image distance $d = f = R/2$. The linear diameter of the image is $D_{image} = d \times \theta = (R/2)\theta$. The radius of the image is $r_{image} = D_{image}/2 = R\theta/4$. The area of the image is $A = \pi r_{image}^2 = \pi (R\theta/4)^2 = \frac{\pi R^2 \theta^2}{16}$.