Question

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the order side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. The focal length of convex mirror is

• A. 25 cm
• B. 50 cm
• C. 100 cm
• D. 12.5 cm

Answer 1

The correct option is A 25 cm

$\begin{array}{c}\text{For convex lens}\\ \begin{array}{c}u=-12cm,f=10cm\\ \text{As}\frac{1}{v}-\frac{1}{u}=\frac{1}{f},\\ \frac{1}{v}=\frac{1}{10}-\frac{1}{12}\\ v=60cm\end{array}\end{array}$

$\begin{array}{c}\text{Now the image of object formed by convex lens is I at a}\\ \text{distance of 60cm from lens.}\\ \text{For convex mirror}\\ \text{Now I, acts as an object form (convex mirror) and forms}\end{array}$$\begin{array}{c}\text{image I at o itself, means the rays after reflection from}\\ \text{the mirror retrace the paths, i.e. these rays incident normally}\\ \text{on mirror. This is possible only if I, is at center of curvature}\end{array}$

$\begin{array}{cc}\text{of}M\text{. Thus Radius of Curvature}R& =M{I}_1\\ & =50cm\\ \text{So focal length of Convex mirror}& =\frac{R}{2}=25cm.\end{array}$