Microtubules are filamentous structures in cells that maintain cell shape and facilitate the movement of molecules within the cell. They are long, hollow cylinders with a diameter of about 25 nm. It is possible to incorporate fluorescent molecules into microtubules; when illuminated by an ultraviolet light, the fluorescent molecules emit visible light that can be imaged by the optical system of a microscope. Required:
If the emitted light has a wavelength of 550nm and the NA of the microscope objective is 1.3, what is the smallest resolvable separation between two objects in the microscope?

the smallest resolvable separation between two objects in the microscope is 2.58 × 10⁻⁷ m

Explanation:

Given the data in the question;

the smallest resolvable separation distance between two objects in the microscope can be determined using the following quation;

= Dλ/NA = (0.61)λ /NA

where λ is the wavelength of emitted light  = 550nm = 5.5 × 10⁻⁷ m

NA = microscope objective = 1.3

so we substitute

= (0.61)5.5 × 10⁻⁷ m) / 1.3

 = 0.0000003355 / 1.3

 = 2.58 × 10⁻⁷ m

Therefore,  the smallest resolvable separation between two objects in the microscope is 2.58 × 10⁻⁷ m

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