Question

a circular plate of radius r is placed on the principal axis at distance f from a convex mirror of focal length f, such that the principal axis passes through the centre of plate normally. the area of image of the plate is

Answer 1

Answer:

Step-by-step explanation:

The mirror formula is $1/v+1/u=1/f$, where u,v and f are the distances of the object and image from the lens and the focal length respectively.

⇒$1/v = 1/f-1/u=(u-f)/uf$.

⇒$v = uf/(u-f)$.

The magnification is $M=h_{i} /h_{o} =-v/u$, where hi and ho are the heights of the image and object respectively.

⇒$M=hi/ho=-v/u=-f/(u-f)=f/(f-u)$.

As per the new Cartesian convention, distances from the mirror on the side of the object are negative and distances on the other side are positive.

⇒ For a convex mirror, u is negative while f and v are positive.

It is is given that the distance of the object from the mirror is equal to the focal length.

⇒u=−f⇒−u=f

⇒M=f/(f−u)=1/2.

⇒ This means that the radius of the image of the plate will be halved.

Hence new radius = r/2

Therefor The area of the image of the plate would be  π(r²/4)