Question

A lens is designed to work in the visible, near-infrared, and near-ultraviolet. The best resolution of
this lens from a diffraction standpoint is
A) in the near-ultraviolet.
B) indeterminate.
C) equal for all wavelengths.
D) in the visible.
E) in the near-infrared.

Answer 1

Concepts and reason

The main concept used to solve this problem is Rayleigh Criterion.

Initially, write the wavelengths corresponding to visible, near-infrared, and near-ultraviolet rays. Then, write the equation of resolution using Rayleigh criterion in terms of wavelength. Finally, compare resolution based on wavelengths.

Fundamentals

Resolving power is defined as the smallest distance between two separate points of an object which is distinguishable when seen with the help of an optical instrument.

Consider that the diffraction is through a circular aperture. Then, the angular resolution is,

$\theta = \frac{{1.220\lambda }}{D}$

Here, $\theta$ is angular resolution, $\lambda$ is wavelength, and D diameter of lens’ aperture.

Shorter wavelength will yield higher resolution.

The smaller wavelength will lead to resolve smaller things with finer details.

The range of wavelength ${\lambda _{{\rm{visible}}}}$ of visible spectrum is,

${\lambda _{{\rm{visible}}}} = \left( {400 - 700{\rm{ nm}}} \right)$

The range of wavelength ${\lambda _{{\rm{IR}}}}$ of near-infrared spectrum is,

${\lambda _{{\rm{IR}}}} = \left( {700{\rm{ nm}} - 1{\rm{ mm}}} \right)$

The range of wavelength ${\lambda _{{\rm{UV}}}}$ of near-ultraviolet spectrum is,

${\lambda _{{\rm{UV}}}} = \left( {10{\rm{ nm}} - 400{\rm{ nm}}} \right)$

The angular resolution is,

$\theta = \frac{{1.220\lambda }}{D}$

The angular resolution depends on the wavelength. So, resolution cannot be equal for all wavelength.

The best resolution can be determined based on the wavelength of the visible, UV rays, and IR rays. Thus, it cannot be indeterminate.

The range of wavelength of visible spectrum is $\left( {400 - 700{\rm{ nm}}} \right)$ . The range of wavelength of near-infrared spectrum is $\left( {700{\rm{ nm}} - 1{\rm{ mm}}} \right)$ . The range of wavelength of near-ultraviolet spectrum is $\left( {10{\rm{ nm}} - 400{\rm{ nm}}} \right)$ .

Compare above wavelengths.

The shortest among visible, Infrared, and Ultraviolet is Ultraviolet having wavelength in the range $\left( {10{\rm{ nm}} - 400{\rm{ nm}}} \right)$ .

Shorter wavelength will yield higher resolution.

Here, the shortest wavelength is Ultraviolet ray. So, the resolution will be highest for Ultraviolet rays. Hence, resolution cannot be highest for visible and Infrared rays.

Ans:

The best resolution from diffraction standpoint is in the near-ultraviolet.