# Optics & Resolution: Can I See the Peak?

• Niles
In summary, the conversation is discussing how to determine if a peak at 100 MHz will be visible with a spectrometer that has a resolution of 0.5 nm. The peak is located at 100 MHz with a full width half maximum of 100 MHz. To determine if the peak will be visible, the wavelength range of the peak is converted into frequency and compared with the spectrometer's resolution. It is also mentioned that detecting the peak is different than resolving its width. The speed of light in a medium is c/n and is used in the equation λf =c/n.

#### Niles

Hi

Say I have a peak of about 100 MHz, and my apparature has a resolution of about Δλ 0.5 nm. How can I find out whether I will see the peak or not?

It's not clear from your post: is the peak located at 100MHz, or is that the full width half maximum? You have a certain wavelength resolution, but what is the mean wavelength?

100 MHz is the FWHM. We are in the visible range, so λ ~ 500 nm (sorry, I should have specified that first).

Ok.

Here's what I would do: convert the FWHM into a wavelength range: do this by converting 500nm into frequency, then add +/- 50 MHz, and convert back to wavelengths. Then you can compare directly with the wavelength resolution of your spectrometer.

Something to keep in mind- detecting the peak is different than resolving the peak width.

I would compare Δf/f (=λ·Δf/c) with Δλ/λ (=0.001).

You need Δf/f > Δλ/λ in order to resolve the peak.

(In case it's not clear from the context of this thread, Δf is the FWHM of the peak, and Δλ is the spectrometer resolution.)

Thanks to both of you. Redbelly98, isn't Δf/f =λ·Δf/c only valid in vacuum?

Strictly speaking, yes. It's a reasonable approximation in air as well. What medium does your spectrometer operate in?

In air. But what is the general version of λf =c?

The speed of light in a medium is c/n, so
λf =c/n
where λ is the wavelength in the medium.

## What is the relationship between optics and resolution?

The quality of an optical system, such as a microscope or telescope, directly affects its ability to produce clear and detailed images. This is known as resolution, and it is crucial in scientific research and other fields where precise observations are necessary. Essentially, the better the optics, the higher the resolution.

## What factors affect the resolution of an optical system?

There are several factors that can impact the resolution of an optical system. These include the quality and design of the lenses, the wavelength of light being used, and any distortions or aberrations in the system. Additionally, the amount of light available and the size of the aperture can also play a role in resolution.

## Can optics alone improve the resolution of an image?

No, optics alone cannot improve the resolution of an image. While high-quality optics can certainly help, there are several other factors that also contribute to the resolution of an image. These include the quality of the sample being observed, the lighting conditions, and the ability of the detector or camera to capture the image.

## Is it possible to see the peak of a very small object using optics?

Yes, it is possible to see the peak of a very small object using optics. However, this depends on several factors such as the wavelength of light being used, the quality of the optics, and the magnification of the system. In general, the smaller the object, the more challenging it is to see its peak.

## How do scientists use optics and resolution in their research?

Scientists use optics and resolution in a variety of ways in their research. For example, they may use high-resolution microscopes to examine cells and tissues, or powerful telescopes to study distant galaxies. They may also use advanced imaging techniques, such as confocal microscopy, to achieve even higher resolutions and produce detailed images for their research.