question_answer

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is

A)  10 cm  

B)  15 cm  

C)  2.5 cm

D)  5 cm

Correct Answer: D

Solution :

By mirror formula, image distance of A \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\] \[\frac{1}{{{v}_{A}}}+\frac{1}{u}=\frac{1}{f}\] \[\frac{1}{{{v}_{A}}}+\frac{1}{(-30)}=\frac{1}{-10}\] \[{{v}_{A}}=-15\,cm\] Also image distance of C \[{{v}_{C}}=-20\,cm\] The length of image        \[=|{{v}_{A}}-{{v}_{C}}|\]                                                 \[=|-15-(-20)|\]                                                 \[=5\,cm\]