The focal length of a concave mirror is $50 \ cm$. At what distance (in $cm$) should an object be placed to obtain a real and inverted image of double the size?

$A$ concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6 \ cm$,find the shift of the screen and the focal length of the mirror.

Incident parallel rays make an angle of $5^{\circ}$ with the axis of a concave mirror of focal length $20 \ cm$. The perpendicular distance of the image from the axis is nearly $-$ (in $cm$)

$A$ small linear object is placed on the optical axis of a concave mirror. If the distance of the nearest end of the object from the mirror is greater than the radius of curvature,then:

$A$ concave shaving mirror has a radius of curvature of $35.0 \, cm$. It is positioned so that the upright image of a man's face is $2.5 \, times$ the size of the face. How far is the mirror from the face in $cm$?

$A$ 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?