Two identically built microscopes are being used to characterize sub-micron features with two different laser sources. The first microscope uses a laser at 632 nm (red), and the smallest feature it can measure is 500 nm. If the second microscope uses a laser at 543 nm (green), what is the smallest feature it can measure

Explanation:

Given:

wavelength used by the first microscope,

resolving power of the first microscope,

wavelength used by the second microscope,

For the microscopes the resolving power is given as:

where:

wavelength of the laser source used

numerical aperture of the microscope

smallest feature that can be distinguished using the optical device

For the first microscope:

Since both the optical device are identically built we will have:

Now for the second optical device:

d is the correct answer

if they have a finite resultant