For a point object,which of the following always produces a virtual image in air?

$A$ candle of height $3 \ cm$ is placed at $300 \ cm$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9 \ cm$. Then $x$ is $.... \ cm$.

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately $0.009$. The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature $0.4 \ m$ is

An object is placed in front of a spherical mirror, and a $2$ times magnified image is formed on a screen. Choose the $\text{CORRECT}$ option.

Write the mirror equation for a spherical mirror.

The separation between the screen and a concave mirror is $2r$. An isotropic point source of light is placed exactly midway between the mirror and the screen. The mirror has a radius of curvature $r$ and reflects $100\%$ of the incident light. Find the ratio of illuminances on the screen with and without the mirror.