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

Answer» <html><body><p></p>Solution :For convex lens `1/v-1/(-12)=1/10` <br/> i.e., v=60 cm i.e., in the absence of convex mirror. Convex lens will <a href="https://interviewquestions.tuteehub.com/tag/form-996208" style="font-weight:bold;" target="_blank" title="Click to know more about FORM">FORM</a> the image `I_1` at a <a href="https://interviewquestions.tuteehub.com/tag/distance-116" style="font-weight:bold;" target="_blank" title="Click to know more about DISTANCE">DISTANCE</a> of 60cm behind the lens. Since the mirror is at a distance of 10cm from the lens `I_1` will be at a distance of 60-10=50 cm from the mirror, i.e., `MI_1=50 cm` <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XII_V02_A_C02_SLV_058_S01.png" width="80%"/> <br/> Now as the <a href="https://interviewquestions.tuteehub.com/tag/final-461168" style="font-weight:bold;" target="_blank" title="Click to know more about FINAL">FINAL</a> image `I_2` s formed at the object O itself, the rays after reflection from the mirror retraces its <a href="https://interviewquestions.tuteehub.com/tag/path-11833" style="font-weight:bold;" target="_blank" title="Click to know more about PATH">PATH</a> i.e., rays on the mirror are <a href="https://interviewquestions.tuteehub.com/tag/incident-1039786" style="font-weight:bold;" target="_blank" title="Click to know more about INCIDENT">INCIDENT</a> normallly i.e., `I_1` is the centre of the mirror , so that `R=MI_1=50 cm and ` hence `F=(R//2)=(50//2)=25 cm`</body></html>


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