Microtubules are filamentous structures in cells that...

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 $25 \mathrm{nm} .$ 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. If the emitted light has a wavelength of $500 \mathrm{nm}$ and the NA of the microscope objective is 1.4 can a biologist looking through the microscope tell whether she is looking at a single microtubule or at two microtubules lying side by side?

Key Concepts

Numerical Aperture

A dimensionless number that characterizes the range of angles over which the microscope objective can accept light. A higher numerical aperture allows for better resolution because it collects more light and permits capturing finer details, which is critical when trying to resolve structures at the nanoscale.

Abbe Criterion

A formula used to estimate the resolving power of an optical system. It defines the minimum distance between two points that can be distinguished as separate entities, relying on the illumination wavelength and the numerical aperture. This concept is central when assessing whether structures such as microtubules can be individually resolved in microscopy.

Fluorescence Microscopy

A technique used to study structures within cells by tagging specific components with fluorescent molecules that emit light upon excitation. This method is crucial for visualizing small cellular structures that are otherwise difficult to see under normal light, and the emitted light’s wavelength plays an important role in determining the resolution and clarity of the image.

Diffraction Limit

A fundamental property of optical systems where the resolution is limited by the bending of light waves. This limit determines the smallest distance between two distinct objects that can be distinguished, and is determined by the wavelength of the light used and the numerical aperture of the microscope objective.

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