**Core Concept**
The Revised National Tuberculosis Control Programme (RNTCP) is a government initiative to control tuberculosis in India. The programme emphasizes the importance of microscopy in diagnosing TB. A designated microscopy centre (DMC) is a healthcare facility equipped with the necessary infrastructure and trained personnel to perform sputum microscopy for detecting TB.

**Why the Correct Answer is Right**
The RNTCP guidelines recommend the establishment of DMCs to ensure timely and accurate diagnosis of TB. These centres are equipped with microscopes and trained staff to perform Ziehl-Neelsen staining on sputum samples. The presence of acid-fast bacilli in the sputum sample indicates the presence of TB. The DMCs also provide training and quality control measures to ensure the accuracy of the microscopy results.

**Why Each Wrong Option is Incorrect**
**Option A:** This is not a correct statement as the RNTCP guidelines do not specify the exact number of DMCs required per district or population size.
**Option B:** This is not a correct statement as the RNTCP guidelines do not recommend a specific type of microscope for use in DMCs.
**Option C:** This is not a correct statement as the RNTCP guidelines do not specify a specific population size or number of patients required to establish a DMC.

**Clinical Pearl / High-Yield Fact**
It is essential to note that the RNTCP guidelines emphasize the importance of quality control measures in DMCs, including regular training and proficiency testing of microscopy technicians.

**Correct Answer: C. 10000**