A researcher is interested in estimating the population of India in 2050 and is developing mathematical models to forecast changes in age composition and population growth. Which field is the researcher most directly working in?

Formal demography

The correct answer is Option 3: Formal demography.

The key clue in the question is the emphasis on forecasting, measurement, age composition, and mathematical models. Formal demography is concerned with the quantitative analysis of population change and has developed sophisticated statistical and mathematical techniques for estimating future population trends. The focus here is on measurement rather than on the social causes or consequences of population change.

Other Options:

Option 1: Social demography. Incorrect. Social demography is more interested in understanding the social, economic, and political factors that influence population trends.

Option 2: Population studies. Incorrect. Population studies is broader and investigates the causes and consequences of population change rather than focusing primarily on measurement and forecasting.

Option 4: Comparative sociology. Incorrect. The question deals specifically with demographic analysis rather than comparison of societies.

NCERT: "Sometimes a distinction is made between formal demography and a broader field of population studies. Formal demography is primarily concerned with the measurement and analysis of the components of population change. Its focus is on quantitative analysis for which it has a highly developed mathematical methodology suitable for forecasting population growth and changes in the composition of population. Population studies or social demography, on the other hand, enquires into the wider causes and consequences of population structures and change. Social demographers believe that social processes and structures regulate demographic processes; like sociologists, they seek to trace the social reasons that account for population trends".