(i) Calculation of position of image
The height of object is 2 cm and that of real image is 3 cm. So, we will first calcualte the magnification by using the formula :
`m=H_(2)/h_(1)`
Please note that an object is always placed above the axis, so the height of a real image is taken as negative and written with a minus sign.
Here, Height of real image. `h_(2) = - 3 cm`.
Height of object, `h_(1) = +2 cm`
So, putting these values in the above magnification formula, we get :
`"Magnification, " m=(-3) /(+2)`
or m= -1.5
Now, we have another magnification formula for mirrors, which is :
`m=v/u`
Here, Magnification, m= -1.5 (Found above)
Image distance, v = ? (To be calculated)
and Objuct distance, u = -16 cm (To the left of mirror )
So, putting these values in the above formula, we get :
`-1.5=-v/((-16))`
`" or "-1.5=v/(16)`
`"So, "v = -1.5 xx 16`
`"or "v = -24 cm`
Thus, the position of image is 24 cm in front of the mirror, to the left of mirror (The minus sign shows that the image is on the left side of the mirror).
(ii) Calculation of focal length
Here, Object distance, u = - 16 cm
Image distance, u = - 24 cm
Focal length, f = ? (To be calculated )
Now, putting these values in the mirror formula :
`1/v+1/u=1/f`
`"We get : "1/(-24)+1/(-16)=1/f`
`"or "-1/24-1/(-16)=1/f`
`(-2-3)/(48)=1/f`
`-5/48=1/f`
`f=-(48)/5`
`"So, Focal length, " f = -9.6 cm`
