VZ = 10 V
Vin = 24 V
The rated maximum Zener current,
\(I_{Z} = \frac{P_{Z}}{V_Z}\)
\(= \frac{500 mW}{10 V}\)
\(= 50 \ mA\)
The minimum current limiting resistance,
\(R = \frac{V_{in} - V_Z}{I_{Z}}\)
\(= \frac {24 V- 10V}{0.05 A}\)
\(= \frac{14V}{0.05A}\)
\(= 280 \Omega\)