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

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

Answer 1

The diameter of the objective needed to resolve two objects only 350 nm apart is approximately 2.18 mm.

Step-by-step explanation:

To calculate the diameter of the objective needed to resolve two objects only 350 nm apart using a microscope with a focal length of 1.5 mm and light of wavelength 550 nm, we can use the Rayleigh criterion for resolution:

Resolution (R) = 1.22 * (wavelength / numerical aperture)

where the numerical aperture (NA) is related to the diameter of the objective (D) and the focal length (f) by:

Numerical Aperture (NA) = D / (2 * f)

Given that the desired resolution is 350 nm (0.35 μm) and the wavelength of light is 550 nm (0.55 μm), we can rearrange the equations to solve for the objective diameter (D):

Resolution (R) = 1.22 * (0.55 μm / NA)

NA = D / (2 * 1.5 mm)

Substitute the given values:

0.35 μm = 1.22 * (0.55 μm / (D / (2 * 1.5 mm)))

Now, let's solve for D:

D = 2 * 1.5 mm * (0.55 μm) / (1.22 * 0.35 μm)

D ≈ 2.18 mm

So, the diameter of the objective needed to resolve two objects only 350 nm apart is approximately 2.18 mm.