Question

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

Answer 1

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.