$A$ concave mirror of focal length $15\, cm$ forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be........$cm$

$A$ short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$, then the ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume $l << X$ and $l << F$):

Where should an object be placed in front of a concave mirror of focal length $20\,cm$ so that the image is $2\,\times$ the size of the object?

Write the mirror equation for a spherical mirror.

Derive the relationship between the focal length $(f)$ and the radius of curvature $(R)$ for a spherical mirror.

$A$ square wire frame of side length $3.0 \, cm$ is placed $25 \, cm$ away from a concave mirror of focal length $10 \, cm$. The center of the wire frame is on the axis of the mirror,with two of its sides perpendicular to the axis. The area of the image will be $..... \, cm^2$.