0
$\begingroup$

In my textbook there is a question as follows:

A diffraction grating with 200 lines per mm is placed between a monochromatic light source and a screen. The distance from the grating to the screen is 2.5 m and the distance between the two 2nd order images is 60 cm on the screen. Calculate the wavelength of the monochromatic light.

$$d=5x10^{-6}m$$

$$y=0.3m$$ $$x=2.5m$$ $$n=2$$ $$sin\theta =\frac{y}{\sqrt{x^2+y^2}}$$ $$\lambda=\frac{d sin\theta}{n}=297 nm$$

But the human eye cannot see 300 nm and shorter wavelengths.

Is there something happening due to the presence of the grating and the screen that allows viewing of these images or would these images not be viewable to the human eye as I suspect ?

My understanding is that the images are not viewable by the human eye.

I also understand that the point behind the question is just to practice using the formula and to not worry too much about the numbers. But I like to think about the real situation when I work through problems.

$\endgroup$
4
  • 4
    $\begingroup$ But the example doesn't suggest that the pattern is viewed directly by human eyes. It can be recorded by a photographic film, an electronic light sensor etc. $\endgroup$
    – Ruslan
    Mar 17, 2023 at 16:19
  • $\begingroup$ @Ruslan That's true Ruslan. But do you agree that for 300 nm viewing with the human eye is impossible ? $\endgroup$
    – Kantura
    Mar 17, 2023 at 17:13
  • 3
    $\begingroup$ There is nothing special about a diffraction grating that would allow the human eye to see 300nm light. A human would not be able to see the diffraction pattern. $\endgroup$ Mar 17, 2023 at 17:20
  • 2
    $\begingroup$ @Kantura with intact human eyes it's impossible. Aphakic eyes might be able to see it. $\endgroup$
    – Ruslan
    Mar 17, 2023 at 17:59

1 Answer 1

3
$\begingroup$

No, the human visual system cannot perceive light shorter than 400 nm.

In a common lab experiment, light from a hydrogen discharge lamp is sent through a diffraction grating and separated into its constituent wavelengths. There are 4 that are nominally in the range of human vision, the shortest wavelength being 410 nm. In my experience, the 410 nm line is just barely on the edge of visible. Many students are unable to see it at all. In my younger days I could see it pretty well if the room was dark and my eyes were properly dark-adapted, especially if I looked off to one side a little, but nowadays I have more trouble seeing it.

If there is any human who can see light of shorter wavelength than this, they would have to be an extreme outlier. To see 297 nm would require a fundamentally different visual system than most humans, and to my knowledge this has never been documented. People with artificial lenses can do better than average, because they filter UV less than our natural ones, but even so, 297 nm seems extreme.

On the other hand, if the screen has chemicals in it that phosphoresce, it could convert the 297 nm light to a wavelength in the visible range, and in that way you could in principle see the line on the screen. You just wouldn't be seeing it at its original wavelength. X-ray machines sometimes use a trick similar to this - the X-ray images themselves are invisible, but a phosphorescent film converts them into visible light that can then be imaged more easily with film or a digital detector (or seen with the naked eye). (Originally the X-rays would just expose the film directly, but by converting them to visible light first you can use much shorter exposure times because the film is much more sensitive in the visible range.)

Also, it's possible the eye can react to UV light without seeing it, for example producing a squinting reflex on a cloudy day that doesn't seem like it should be bright enough to have to squint, but although this would technically be a kind of unconscious perception, I don't think I would categorize it as "seeing," and you wouldn't be able to exploit it to visualize the line on the screen that you're talking about.

$\endgroup$
1
  • 2
    $\begingroup$ Unless the transmission grating is specifically made for UV wavelength using polymers like acrylic and silicone, ceramics and glasses like quartz and fused silica, the UV will be absorbed by the grating. Use of a reflection grating and a fluorescent screen enables a simple experiment to be set up to observe a UV spectrum. $\endgroup$
    – Farcher
    Mar 17, 2023 at 22:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.