Question

a point object is placed at a distance 30cm from a convex lens of power + 4d.it is observed that when a convex mirror is kept on right from the lens the image of the object coincides with the object itself. what is the focal length of mirror

Answer 1

Dear Student ,

it means that the image will form at the focus of the mirror if mirror s absent .
let the focal length of the mirror be f
u=-30
focal length of the convex lens F=100/4=25 cm .
$$\begin{gathered} v=f \\ \frac{1}{v}-\frac{1}{u}=\frac{1}{F} \\ \frac{{\displaystyle 1}}{{\displaystyle f}}-\frac{{\displaystyle 1}}{{\displaystyle -30}}=\frac{{\displaystyle 1}}{{\displaystyle 25}} \\ \frac{1}{f}=\frac{1}{25}-\frac{1}{30}=\frac{6-5}{150} \\ f=150cmofthemirror. \\ Regards \end{gathered}$$