Here we have been given the object distance and focal length, so first of all we will find out the image distance which will give us the position of image.
(i) Position of image
Here, Object distance, u= -15 cm ( To the left of mirror )
Image distance, v = ? (To be calculated )
And, Focal length, f = -10 cm (It is concave mirror )
Now, putting these values in the mirror formula :
`1/v+1/u=1/f`
`"we get : "1/v+1/-15=1/-10`
` or" "1/v-1/15=-1/10`
`"or " 1/v=-1/101/15`
`1/v=(-3+2)/30`
`1/v=-1/30`
`"So, Image distance, "v= -30 cm`
Thus, the position of image is 30 cm to the left side of mirror or 30 cm in front of mirror (Minus sign shows the left side of morror ).
(ii) Nature of image. Since the image in fornt of the concave mirror, its nature will be "Real and Inverted".
(iii) Size of image. To find the size of image, we will have to calculate the magnification first. The magnification produced by a mirror is given by :
`m=-v/u`
Here, Image distance, v = -30 cm
Object distance, u = -15 cm
`"So, "m=-((-30))/((-15))`
`m=-30/15`
Magnification, m=-2
We also have another formula for magnification, which is :
`m=H_(2)/H_(1)`
Here, Magnification, m= -2 (Found above )
Height of image, `H_(2) = ?` (To be calculate )
Height of object, `H_(1) = 1 cm` (Given)
Now, putting these values in the above magnigication formula, we get :
`-2 = h_(2)/1`
`"So, Height of image, "H_(2)=-2xx1`
=-2 cm
Thus, the size of image is 2 cm long. The minus sign here shows that the image is formed below the principle axis. That is, it is a real and inverted image.
