An object of length 10 cm is placed at right angles to the principal axis of a mirror of radius of curvature 60 cm such that its image is virtual, erect and has a length 6 cm. What kind of mirror it is and also determine the position of the object ?

Explanation

Since the image is virtual, erect and of a smaller size, the given mirror is
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convex.(concave mirror does not form an image with the said description).
Given `R= +60 cm f= (R )/( 2) =30 cm`
Transverse magnification,
` m=(1)/(O) = (6)/(10) =+ (3)/(5 ) ` further `m=-(v)/(u ) = 3/5`
` therefore v= ( 3u )/(5) `
using `(1)/(v ) + (1 )/(u ) = (1)/(f) " " (-5)/(3u ) +(1)/(u ) = (1)/(30)`
`(-5+3)/( 3u) = (1)/(30) therefore u=- 20 cm `
Thus the object is at a distance 20 cm (from the pole) in front of the mirror.