question_answer

A luminous object is placed 20 cms from the surface of a convex mirror and a plane mirror is get so that the virtual images formed in the two mirrors coincide. If the plane mirror is at a distance of 12 cms from the object, then the focal length of the convex mirror is

A)  10 cm                  

B)         5 cm  

C)  20 cm                  

D)         40 cm

Correct Answer: B

Solution :

 The situation is as shown in the figure below : For plane mirror\[,\]\[v=u\]. So, the image will be formed at a distance of\[12\,\,cm\]from the plane mirror. This image is therefore at a distance of\[24\,\,cm\]from the object. Distance between the object and the convex mirror is\[20\,\,cm\]. So the distance between the pole of convex mirror and the image is\[24-20=4\,\,cm\]. Being on the right side of the convex mirror this image distance will be taken as positive. So, for the convex mirror\[u=-20\,\,cm\]and\[v=+4\,\,cm\] \[\therefore \]  \[\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{4}-\frac{1}{20}=\frac{4}{20}\mathbf{=}\frac{\mathbf{1}}{\mathbf{5}}\]