Physics · Wave Optics · NEET
No. Magnification only makes the image bigger. Resolving power is about detail: can you see two close points as two separate points? A microscope can magnify a blur into a bigger blur with no new detail. Beyond the resolving limit, extra magnification is called empty magnification. So high magnification without high resolving power is useless.
Resolving power RP = 2 n sinB / (1.22 lambda). Here lambda is the wavelength of light used, n is the refractive index of the medium between the object and the objective lens, and B is the half-angle of the light cone entering the objective. The quantity n sinB is called the numerical aperture (NA). The smallest distance it can resolve is d = 1.22 lambda / (2 n sinB).
Resolving power is proportional to 1/lambda. Diffraction spreads light less when the wavelength is smaller, so the diffraction discs of two nearby points stay separate. That is why we use blue light or UV and electron microscopes for fine detail: a smaller lambda means a smaller limit of resolution d, so finer objects can be seen distinctly.
The limit of resolution is the smallest distance d between two points that can still be seen as two. It is the reciprocal of resolving power: d = 1.22 lambda / (2 n sinB). A smaller d means a better microscope. Note the microscope limit depends on the distance d, while the telescope limit is an angle 1.22 lambda / D. Do not mix them up.
Two ways: use light of smaller wavelength (blue instead of red, or UV), and increase the numerical aperture n sinB. NA is raised by using a wide-cone objective (large B) and by placing an oil of high refractive index n between the object and the lens. This is why oil-immersion objectives are used in biology labs.
For a microscope, we write it using numerical aperture (n sinB), not the plain diameter D. The diameter form 1.22 lambda / D is used for a telescope, where the object is far away. Confusing the two is a common exam mistake. For a microscope think numerical aperture; for a telescope think objective diameter.
The ratio of resolving powers of an optical microscope for two wavelengths lambda1 = 4000 A and lambda2 = 6000 A is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
n sinB is the numerical aperture (NA). n is the refractive index of the medium between object and objective; B is the half-angle of the cone of light collected by the objective. A larger NA collects more diffracted light and gives higher resolving power.
Oil has a high refractive index n (about 1.5) compared to air (1.0). Placing oil between the sample and the objective raises the numerical aperture n sinB, which increases resolving power and lets you see finer detail.
It is set by a distance. The limit of resolution is the smallest separation d = 1.22 lambda / (2 n sinB) between two points. The telescope limit, by contrast, is the smallest angle 1.22 lambda / D.
Electrons have a very small de Broglie wavelength, far smaller than visible light. Since resolving power is proportional to 1/lambda, a tiny lambda gives an extremely high resolving power, so electron microscopes reveal atomic-scale detail.
No. Resolving power depends only on the wavelength lambda and the numerical aperture n sinB. Making the light brighter does not help separate two close points; only a smaller lambda or larger NA does.
