Find the size, nature and position of the image formed when an object of size 1 cm is placed at a distance of 15 cm from a concave mirror of focal length 10 cm.

Explanation

Object distance , `u = -15` cm ( to the left of mirror)
Image distance, `v = ?`
Focal length, `f = - 10 cm` (concave mirror)
Using mirror formula, `(1)/(v) + (1)/(u) = (1)/(f)`
`(1)/(v ) + (1)/(-15) = (1)/(-10) rArr (1)/(15) = (-1)/(10)`
`(1)/(v) = (-1)/(10) + (1)/(15) = (-3 + 2)/(30) = (-1)/(30)`
Thus, image distance, `v = -30` cm (negative sign indicates that the image is on the left side of the mirror).
`therefore` Position of image is 30 cm in front of the mirror. Since the image is in front of the mirror, it is real and inverted.
To find the size of the image, we have to calculate the magnification.
`m = (-v)/(u) = (-(-30) )/( (-15)) = -2`
We know that `m = (h_2)/(h_1)`
Here, height of the object `h_1 = 1 ` cm
`-2 = (h_2)/(1)`
`h_2 = -2 xx 1 =-2` cm
The height of image is 2 cm ( negative sign shows that the image is formed below the principal axis).