Chapter 9

Geometrical and waves optics

Experience of Young's slits

ComplémentAn introductory video

The quantum world for dummies (Young's slit experiment)

The quantum world for dummies (Young's slit experiment)

FondamentalThe device of Young holes (without lenses)

In the device of Young holes, the main source is located on the segment of the mediator joining the two secondary sources.

Interference is observed on a screen parallel to the axis of the two sources.

The device of Young holes (without lenses)

Since the interference is visible on the screen independently of its position, it is called non-localized interference throughout the space.

In practice, -see figure) and it will be observed fringes at points of coordinates closed to , for which and .

The optical path difference between the rays and is equal to (the rays propagate in the air, index is practically equal to ) :

Is :

We do the expansion limited at the second order in , and  :

And so :

Is :

Finally :

And the illumination at point becomes :

The interference fringes are obtained by and thus are straight lines parallel to the axis (Oy).

Young's slits


On the screen, the fringes of the same nature will be separated by a distance called inter-fringe and denoted , which is ultimately the spatial period of cosine which is involved in the intensity :

So :

With holes gape of , diameter of , and a screen placed at , a dozen fine fringes are discernible at the center of a diffraction pattern.

Fringes at the center of a diffraction pattern.
  • , and holes may be replaced by slits (very narrow along Ox) parallel to Oy ; indeed, the atoms (in different positions) of the source located behind the slit emit incoherent wave trains together.

    One can thus summing the illuminations on the screen due to each of these atoms.

    The illumination is not dependent on variable , the luminous intensities will build without blur : the phenomenon will be brighter.

  • is of the order of magnitude of the meter,  millimeter and  micrometer ; the inter-fringe is in the order of the millimeter.

    Thus for the first time, Thomas Young in could measure the wavelengths of light radiation.

FondamentalInstallation of Young's holes with lenses

The classical installation of Young's holes can be improved.

Indeed, the interfering rays at a point of the screen does not have the same intensity.

When passing through a hole, diffraction "spreads" the wave in a cone around the direction of geometrical optics.

The diffracted rays in different directions have no reason to have the same intensity.

The contrast of interference is then not maximal.

Moreover, the most illuminated areas by each hole badly overlap and interference phenomenon is little luminous.

It overcomes these disadvantages by adding two lenses to the device.

The point source is placed at the focus of a CV lens and put the screen in the focal plane of another CV lens .

To draw the figure proposed above, it is necessary to start from a point of the screen and give a ray "construction" which passes through the center of the second lens and inclined at an angle to the optical axis.

The rays that interfere in have much the same intensity as they are inclined at the same angle to the horizontal, which is the direction of propagation of geometrical optics.

The phenomenon is bright around (it is the image of geometrical optics).

Installation of Young's holes with lenses

Determining the path difference :

and holes belong to the same wave surface : the two waves arrive in phase at the holes. Consequently :

Therefore :

The principle of inverse return of light and Malus' theorem can be concluded that :

Therefore :

The angle is small and if  denotes the distance between the two sources :

And the illumination in the focal plane of the second lens :

The result is similar to that obtained without lens.

Distance holes - screen is replaced by the focal length of the lens.

The fringes are rectilinear and of course the inter-fringe is :

ComplémentTwo videos on the Young slits (A The Rille)

Wave tank, centimeter waves, light waves :

Slits Young (Video Alain Le Rille, a teacher in CPGE in Lycée Janson de Sailly, Paris) : wave tank, centimeter waves, light waves


Influence of the width of the source slit :

Slits Young (Video Alain Le Rille, a teacher in CPGE in Lycée Janson de Sailly, Paris) : influence of the width of the slit source
Scalar theory of light, light intensity (illumination)
Observation of double stars