A security mirror used in a big showroom has radius of curvature 5 m. If a customer is standing at a distance of 20 m from the cash counter, find the position, nature and size of the image formed in the security mirror.

Options

A. `{:("Position of image ","Magnification"),("2.22 m in front of the mirror",-0.11):}`
B. `{:("Position of image ","Magnification"),("2.22 m behind the mirror ",+0.11):}`
C. `{:("Position of image ","Magnification"),("1.11 m behind the mirror",+0.22):}`
D. `{:("Position of image ","Magnification"),("1.11 m in front of the mirror ",-0.11"):}`

Answer

B

Explanation

Security mirror is a convex mirror
Radius of curvature R = +5 m
Object distance u = -20 m
Image-distance `V = ? `
Size of image `h. = ?`
Focal length `f = R/2 = 5/2 = + 2.5 m`
(as the principal focus in a convex mirror is behind the mirror).
By applying mirror formula
`1/f = 1/v + 1/u`
`1/v = 1/f - 1/u`
`= 1/25 - 1/((-20))`
`= (40 + 5)/(100)`
`= 45/100`
`v = 100/45`
`= + 2.22 m`
The image is + 2.22 m behind the mirror
`m = - v/u`
`= -(2.22)/(-20)`
`= + 0.11`
The image is smaller in size by a factor of 0.11 Position of image: Behind the mirror
Size of image: diminished