Question

how is the resolving power of a microscope affected when the diameter of the objective lens is decreased?

Answer 1

Before we go into specificity of the question, we have to understand the underlying concept, which is - diffraction due to single slit.We are aware of wave nature of light. Path difference caused by a beam of light entering through edges of a pin-hole might land on a flat imaging screen with some phase difference, and accordingly, it will be decided if the waves would interfere constructively or destructively. And that’s how we get what is called Airy disk. To sum it up, when light has to pass through a pin-hole, on the imaging place you’ll see concentric circles with exponentially decreasing intensities away from the centre.Moving onto the question in hand, in the equation shown in the figure, for small angles, taking a first order approximation of sin(theta) as theta, which in-turn can be approximated to as the ratio of (y/focal length), we’ll see that resolution of the imaging system would be:Directly proportional to wavelength of illuminating light beam.Inversely proportional to the diameter of iris (which in this case is dia. of the lens), andDirectly proportional to the focal length.So,a) Resolution improves if wavelength of light decreases,b) Resolution degrades with decrease of lens diameter.