$A$ convex mirror of radius of curvature $30 \,cm$ forms an image that is half the size of the object. The object distance is: (in $\,cm$)

$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. The image will form at

In a concave mirror experiment,an object is placed at a distance ${x_1}$ from the focus and the image is formed at a distance ${x_2}$ from the focus. The focal length of the mirror would be

You are asked to design a shaving mirror assuming that a person keeps it $10\,cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25\,cm$. The radius of curvature of the mirror would then be.....$cm$.

When an object is placed at a distance of $25 \ cm$ from a concave mirror,the magnification is $m_1$. The object is moved $15 \ cm$ farther away with respect to the earlier position and the magnification becomes $m_2$. If $m_1/m_2 = 4$,the focal length of the mirror is $....... \ cm$ (Assume image is real and $m_1, m_2$ are numerical values).

An object ' $O$ ' is placed at a distance of $100\,cm$ in front of a concave mirror of radius of curvature $200\,cm$ as shown in the figure. The object starts moving towards the mirror at a speed of $2\,cm/s$. The position of the image from the mirror after $10\,s$ will be at ...... $cm$.