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Q). Explain resolving power of a microscope. Compare between telescope and microscope.

Dear student,
 
Kindly ask different queries in different thread. Also, refer the answer os 1st part.

For microscopes, the resolving power is the inverse of the distance between two objects that can be just resolved. This is given by the famous Abbe’s criterion given by Ernst Abbe in 1873 as

$$\begin{gathered} ∆d=\frac{\lambda }{2n \sin \theta } \\ resolving power=\frac{1}{∆d}=\frac{2n \sin \theta }{\lambda } \end{gathered}$$

Where n is the refractive index of the medium separating object and aperture. Note that to achieve high resolution n sin θ  must be large. This is known as the Numerical aperture.

Thus, for good resolution:

1. sin θ  must be large. To achieve this, the objective lens is kept as close to the specimen as possible.
2. A higher refractive index (n) medium must be used. Oil immersion microscopes use oil to increase the refractive index. Typically for use in biology studies this is limited to 1.6 to match the refractive index  of glass slides used. (This limits reflection from slides). Thus the numerical aperture is limited to just 1.4-1.6. Thus, optical microscopes (if you do the math) can only image to about 0.1 micron. This means that usually organelles, viruses and proteins cannot be imaged.
3. Decreasing the wavelength by using X-rays and gamma rays. While these techniques are used to study inorganic crystals, biological samples are usually damaged by x-rays and hence are not used.