An object ABED is placed in front of a concave mirror beyond the center of curvature C as shown in figure., State the shape of the image.

Options

A. `|m_(AB)|lt1 and |m_(ED)|lt1`
B. `|m_(AB)|gt1 and |m_(ED)|lt1`
C. `|m_(AB)|lt1 and |m_(ED)|gt1`
D. `|m_(AB)|gt1 and |m_(ED)|gt1`

Answer

a.

Explanation

Objec t is placed beyond C. Hence, the image will be real and it will lie between C and F. Further u, and v are negative, hence the mirror formula will become
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/(u)=(1)/(f)=(u-f)/(uf) or v=(f)/(1-(f//u))`
Now, `u_(AB) gt u_(ED)`
`:.u_(AB) gt v_(ED)`
`|m_(AB)| lt |m_(ED)| (" as" m=-(v)/(u))`
Therefore, shape of the image will be as shown in figure.
Also, note that, `v_(AB) lt u_(AB) and v_(ED) lt u_(ED)`,
So, `|m_(AB)| lt 1` and `|m_(ED)| lt 1`