Since the virtual image is 3 times the height of the size of the object, then `h_i=3h_0` , where `h_i` is the image height and `h_o` is the object's height.
Base on this, the magnification factor (m) of the mirror is:
`m=h_i / h_o = (3h_o)/h_o=3`
Moreover, magnification factor is equal to the negative ratio of image distance (`d_i` ) and object's distance (`d_o` ) from the mirror.
`m=-d_i / d_o`
Expressing `d_i` in terms of `d_o` result to:
Then, apply the mirror equation to solve for `d_o` .
`1/d_o + 1/d_i = 1/f`
Substitute `d_i=-3d_o` and f=30 cm to the formula.
`1/d_o + 1/(-3d_o) = 1/30`
`1/d_o - 1/(3d_o)=1/30`
To simplify the equation, multiply both sides by the LCD which is 30d_o.
`30d_o*(1/d_o - 1/(3d_o))=1/30*30d_o`
`30 - 10=d_o`
Hence, the object is placed at a distance of 20 cm from the concave mirror.