A

Step 1: For a black spherical object, the power absorbed due to the nuclear source is given by the Stefan-Boltzmann law: \( P = \sigma A T^4 \), where \( A \) is the surface area of the sphere and \( \sigma \) is the Stefan-Boltzmann constant.
Step 2: With the thermal protection shield, the system can be treated as two black bodies in series. The temperature of the probe will be affected by the added thermal barrier.
Step 3: Assuming a uniform temperature distribution, the effective temperature of the probe plus one shield can be modeled using the effective thermal resistance. For one black shield, the new surface temperature \( T' \) of the probe can be expressed as \( T' = T \left(\frac{1}{2} \right)^{1/4} = T \cdot \left( \frac{1}{\sqrt{2}} \right) = \frac{T}{\sqrt{2}}.
Step 4: Extending this logic, with \( N \) shields, the temperature of the probe would further decrease: \( T_{N} = T \cdot \left(\frac{1}{\sqrt{2}} \right)^{N}.
Therefore, the final expression shows that the probe's surface temperature decreases with the number of shields, producing a perfectly insulated effect with increasing layers.