Question

the image formed by a convex mirror focal length 20cm is a quarter of the object . what is the distance of the object from the mirror​

Answer 1

Answer:

The mirror formula is 1v+1u=1f1v+1u=1f where, u,vu,v and ff are the distance of the object from the mirror, the distance of the image from the mirror, and, the focal length, respectively.

The distance from the mirror towards the side of the object is taken as negative and the distance to the other side is taken as positive.

The magnification is hiho=−vu,hiho=−vu, where, hihi and hoho are the height of the image and the height of the object, respectively.

The distance above the principal axis is taken as positive and the distance below the principal axis is taken as negative.

It is given that the magnification is 14.14. The magnification is positive since the image formed by a convex mirror is virtual and hence erect.

⇒−vu=14⇒v=−u4.⇒−vu=14⇒v=−u4.

1v+1u=1f⇒−4u+1u=120.1v+1u=1f⇒−4u+1u=120.

⇒−3u=120⇒u=−60.⇒−3u=120⇒u=−60.

⇒⇒ The distance of the object from the mirror is 6060 cm.