Question

In: Physics

A microscope is used to examine a sample of bacteria that are spread on glass. If...

A microscope is used to examine a sample of bacteria that are spread on glass. If the diameter of the objective is twice its focal length and the sample is near the focal point of the objective, determine the shortest distance between two bacteria that can be resolved under the microscope in the terms of the wavelength ? of the light source.
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Expert Solution

The shortest distance between two objects that can be resolved, when viewed with an optical instrument is known as resolution limit d of the instrument. For microscope it is given as,

Here, ? is the wavelength of the light used to illuminate the microscope

NA is numerical aperture for the objective lens and it is given as

Here, n is the refractive index of the medium in which objective lens is placed (For air n =1)

? is the angle of cone of the light coming from objective.

Given:

Diameter of the objective is twice the focal length,

Sample is near focal point

Solution:

From the figure above Numerical aperture can be given as,

For microscope resolution limit is given as,

Substituting the value of numerical aperture in above equation we have,

Thus, the shortest distance between two bacteria that can be resolved under the microscope in the terms of the wavelength ? of the light source is .

genius_generous answered 7 months ago

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