The magnification (m) of a spherical mirror is defined as the ratio of the image height to the object height, and also as the negative ratio of the image distance to the object distance. The formula is expressed as:
\(m=\frac{\text{Height of the image}}{\text{Height of the object}}\)
\(=-\frac{\text{Image distance}}{\text{Object distance}}\)
\(⇒ m=\frac{h_I}{h_o}=\frac{-v}{u}\)
Given the height of the object as \( h_o = h \), and the height of the image formed is \( h_I = −3h \) (indicating a real image), the magnification equation becomes:
\(-\frac{3h}{h}=\frac{-v}{u}\)
\(⇒\frac{v}{u}=3.\)
With an object distance \( u = −10 \) cm, the image distance is calculated as:
v = 3 × (−10) = −30 cm
The negative sign for the image distance signifies that a real, inverted image is formed 30 cm in front of the concave mirror.