A candle is placed $$20$$ cm from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is $$12$$ cm away from the object, what is the focal length of the convex mirror?

Question

Infinity Learn · Accepted Answer

For convex mirror, $$u+v=12$$×$$2=24cm(because$$ for plane mirror, distance of object $$=$$ distance of $$image)$$. Also, here for the convex mirror u : $$20$$ cm, therefore ν $$=$$ $$4$$ cm. Hence, using for plane mirror image distance $$=12$$ cm $$1v+1u=1f$$  ⇒ $$14+1-20=1f$$ We find f $$=$$ $$5$$ cm.Plane mirror is to be placed between the object and the convex mirror.

A candle is placed 20 cm from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is 12 cm away from the object, what is the focal length of the convex mirror?

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