Find the focal length (in $cm$) of a convex mirror whose radius of curvature is $32\, cm$.

$(a)$ What should be the position of the object,when a concave mirror is to be used $(i)$ as a shaving mirror,and $(ii)$ in torches producing a parallel beam of light? $(b)$ $A$ man standing in front of a mirror finds his image having a very small head and legs of normal size. What type of mirror is used in designing such a mirror?

Which of the following ray diagrams is correct for the ray of light incident on a concave mirror as shown in Figure?

An object is placed at a distance of $25 \, cm$ away from a converging mirror of focal length $20 \, cm$. Discuss the effect on the nature and position of the image if the position of the object changes from $25 \, cm$ to $15 \, cm$. Justify your answer without using the mirror formula.

Write down four important characteristics of the image formed by a plane mirror.

If the image formed by a mirror for all positions of the object placed in front of it is always erect and diminished,what type of mirror is it? Draw a ray diagram to justify your answer. Where and why do we generally use this type of mirror?