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An object of length 10 cm is placed at r...

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 ?

Text Solution

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Since the image is virtual, erect and of a smaller size, the given mirror is convex (concave mirror does not form an image with the said description)

Given R=+60 cm `f=R/2=30 cm`
Transverse magnification `m=I/O=6/10= pm 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).
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