Assertion (A) is false. When two waves of equal amplitude and a phase difference of \( \frac{\pi}{2} \) interfere, the resultant intensity is \( I_0 \), which is equal to the intensity of a single wave, not otherwise. The formula for resultant intensity is \( I = 2I_0 \cos^2 \left( \frac{\phi}{2} \right) \). With \( \phi = \frac{\pi}{2} \), this becomes \( I = 2I_0 \cos^2 \left( \frac{\pi}{4} \right) = 2I_0 \times \frac{1}{2} = I_0 \). Therefore, assertion (A) is true. Reason (R) is correct. While resultant intensity in interference can be the sum of individual intensities when the phase difference is non-zero, for a phase difference of \( \frac{\pi}{2} \), the intensities do not simply add; they are affected by interference. Thus, the correct answer is (d), as assertion (A) is false and reason (R) is true.