A point object at 15cm from a concave mirror of radius of curvature 20cm is made it oscillate along the principal axis with amplitude 2mm. The amplitude of its image will be 

 $$\begin{gathered} according to mirror formula\frac{1}{15}+\frac{1}{v}=\frac{2}{20}=\frac{1}{10 } solving v=30 \\ then magnification m= \frac{v}{u}=\frac{30}{15}=2 this is transverse magnification \\ longitudinal magnification \frac{dv}{du}=-\frac{v^2}{u^2}= m^2 =4 \\ so amplitude of image oscillation is 2x4=8 \end{gathered}$$