The lens-maker's formula for spherical surfaces is applied:
\[ \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2-n_1}{R} \]
Given: \( n_1 = 1 \) (air), \( n_2 = 1.5 \) (glass), \( R = 10 \) cm, \( u = -50 \) cm. \( v \) represents the image distance.
Substituting the values:
\[ \frac{1.5}{v} - \frac{1}{-50} = \frac{1.5 - 1}{10} \]
Simplifying the equation:
\[ \frac{1.5}{v} + \frac{1}{50} = \frac{0.5}{10} \]
\[ \frac{1.5}{v} + \frac{1}{50} = 0.05 \]
\[ \frac{1.5}{v} = 0.05 - \frac{1}{50} \]
\[ \frac{1.5}{v} = 0.05 - 0.02 \]
\[ \frac{1.5}{v} = 0.03 \]
Solving for \( v \):
\[ v = \frac{1.5}{0.03} \]
\[ v = 50 \] cm
The image is formed 50 cm within the glass.