Certainly! Please provide me with the conditions you want your circuit to follow, and I'll do my best to guide you through the design process.

For the NE555 timer IC configured in monostable mode to achieve a 10-second delay, you'd generally use the formula $t = 1.1 \cdot R \cdot C$ where (t) is the time in seconds ((10) seconds in your case), (R) is the resistor value in ohms ((\Omega)), and (C) is the capacitor value in farads (F).

Given that you want the light to be on for (10) seconds ((t = 10) seconds), and using the formula, you can rearrange it to solve for (R) and (C).

With (C = 100, \mu F = 100 \times 10^{-6} ,F), \begin{align*} t &= 1.1 \cdot R \cdot C \ 10 &= 1.1 \cdot R \cdot 100 \times 10^{-6} \ R &= \frac{10}{1.1 \cdot 100 \times 10^{-6}} \ R &= 90.9 \times 10^{3} ,\Omega \end{align*}

So, (R \approx 91 ,k\Omega) and (C = 100, \mu F).

Keep in mind that the values provided here are based on choosing a common capacitor value. Depending on the precision you need, you may want to adjust these values or use a potentiometer for fine-tuning the resistance.