1.

A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15cm. Given the location of the image and the magniftication.

Answer»

`6.7cm, 5//9`
`7.5cm,5//9`
`6.7cm,9//5`
`7.5cm,9//5`

Solution :(a) Given, focal length of convex MIRROR `f=+15cm`
(focal length of convex mirror is taken as positive)
DISTANCE of OBJECT `u=-12cm`
Size of object `O=4.5cm`
using the mirror formula
`1/f=1/v+1/u`
`1/15=1/v-1/12`
`implies1/v=1/15+1/12=(4+5)/60=9/60`

Distance of image from the mirror `v=6.7cm`
The positive sign SHOWS that the image is formed behind the mirror.
Using the formula of magnification,
`m=-v/u=L/O`
`(-6.7)/(-12)=l/4.5`
Size of image `l=2.5cm`
As `l` is positive so image is erect and virtual.
Magnification `m` is given by
`m=l/O=2.5/4.5=25/45=5/9`


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