The circular boundary of the concave mirror subtends a cone of half-angle $\theta$ at its centre of curvature. The minimum value of $\theta$ for which a ray incident on this mirror parallel to the principal axis suffers more than one reflection is......$^o$

An object is placed at $(i) \; 10 \; cm$,$(ii) \; 5 \; cm$ in front of a concave mirror of radius of curvature $15 \; cm$. Find the position,nature,and magnification of the image in each case.

$A$ person wants a real image of his own,$3$ times enlarged. Where should he stand in front of a concave mirror of radius of curvature $30 \ cm$ (in $cm$)?

In an experiment to determine the focal length $(f)$ of a concave mirror by the parallax method,a student places the object pin $\text{A}$ on the principal axis at a distance $x$ from the pole $\text{P}$. The student looks at the pin and its inverted image from a distance,keeping his/her eye in line with $\text{PA}$. When the student shifts his/her eye towards the left,the image appears to the right of the pin. Then:

$A$ mobile phone lies along the principal axis of a concave mirror,as shown in the figure. Show by a suitable diagram,the formation of its image. Explain why the magnification is not uniform. Will the distortion of the image depend on the location of the phone with respect to the mirror?

An object is placed at a distance of $18 \ cm$ in front of a mirror. If the image is formed at a distance of $4 \ cm$ on the other side,then the focal length,nature of the mirror,and nature of the image are respectively: