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A microscope with an objective of focal length 1.5 mm is used to inspect the tiny features of a computer chip. It is desired to resolve two objects only 350 nm

What diameter objective is needed if the microscope is used in air with light wavelength 550 nm

User Neil Hoff
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1 Answer

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Answer:

The diameter of the objective needed to resolve two objects only 350 nm apart using the microscope in air with a light wavelength of 550 nm is approximately 1.63 mm.

Step-by-step explanation:

To determine the diameter of the objective needed to resolve two objects that are only 350 nm apart using a microscope in air with light wavelength of 550 nm, we can use the formula for the minimum resolvable distance (the Rayleigh criterion):

Minimum resolvable distance (d) = 1.22 * (λ / NA)

Where:

λ = wavelength of light

NA = numerical aperture of the objective

The numerical aperture (NA) of an objective lens is defined as the measure of its ability to gather light and resolve fine details at a fixed object distance. It is related to the diameter of the objective (D) and the focal length of the objective (f) as follows:

NA = D / (2 * f)

Given that the focal length of the objective (f) is 1.5 mm (or 1.5 * 10^-3 meters) and the wavelength of light (λ) is 550 nm (or 550 * 10^-9 meters), we can calculate the numerical aperture (NA):

NA = D / (2 * f)

NA = D / (2 * 1.5 * 10^-3)

Now, we need to calculate the minimum resolvable distance (d) using the Rayleigh criterion:

d = 1.22 * (λ / NA)

d = 1.22 * (550 * 10^-9) / (D / (2 * 1.5 * 10^-3))

d = 1.22 * (550 * 10^-9) * (2 * 1.5 * 10^-3) / D

Now, let's plug in the value of the desired minimum resolvable distance (350 nm or 350 * 10^-9 meters):

350 * 10^-9 = 1.22 * (550 * 10^-9) * (2 * 1.5 * 10^-3) / D

Now, we can solve for D:

D = 1.22 * (550 * 10^-9) * (2 * 1.5 * 10^-3) / (350 * 10^-9)

D = 1.63 mm

So, the diameter of the objective needed to resolve two objects only 350 nm apart using the microscope in air with a light wavelength of 550 nm is approximately 1.63 mm.

User Umbersar
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