experiments >> malu's law
Intensity and determination of diffraction
A whole gamut of experiments may be done with this experimental setup:
- Huygens principle
In optics, a statement that all points of a wave front of light in a vacuum or transparent medium may be regarded as new sources of wavelets that expand in every direction at a rate depending on their velocities. Proposed by the Dutch mathematician, physicist, and astronomer, Christiaan Huygens, in 1690, it is a powerful method for studying various optical phenomena.
In the illustration of the Huygens principle applied to both plane and spherical waves.
- Each point on the wave front AA1 can be thought of as a radiator of a spherical wave that expands out with velocity c, traveling a distance ct after time t. A secondary wave front BB1 is formed from the addition of all the wave amplitudes from the wave front AA1.
- Huygens' construction of a diffracted wave from a transmission grating. The wave front is constructed by adding spherical waves from each slit of the grating. The wave emitted at a given slit is delayed by one full cycle with respect to the wave from an adjacent slit.
- Interference
- Fraunhofer and Fresnel diffraction
- Fresnel’s zone construction
- Coherence
- Laser
- Airy disk
- Airy ring
- Poisson’s spot
- Babinet’s theorem
- Bessel functions
- Resolution of optical instruments
Principle and procedure:
Pin hole diaphragms and circular obstacles are illuminated with laser light. The resulting intensity distributions due to diffraction are measured by means of a photo diode.
The experiments that may be carried out with the pin-hole experimental setup are:
› The complete intensity distribution of the diffraction pattern of a pin hole diaphragm (D1 = 0.25 mm) is determined by means of a sliding photo diode. The diffraction peak intensities are compared with the theoretical values. The diameter of the pin hole diaphragm is determined from the diffraction angles of peaks and minima.
› The positions and intensities of minima and peaks of a second pin hole diaphragm (D2 = 0.5 mm) are determined. The diffraction peak intensities are compared with the theoretical values. The diameter of the pin hole diaphragm is determined.
› The positions of minima and peaks of the diffraction patterns of two complementary circular obstacles (D*1 = 0.25 mm and D*2 = 0.5 mm) are determined. Results are discussed in terms of Babinet’s Theorem.
Multiple slits which all have the same width and the same distance among each other, as well as transmission grids with different grid constants, are submitted to laser light. The corresponding diffraction patterns are measured according to
their position and intensity, by means of a photo diode which can be shifted.
The experiments that may be carried out with the multiple slits and grid experimental setup are:
› The position of the first intensity minimum due to a simple slit is determined, and the value is used to calculate the width of the slit.
› The intensity distribution of the diffraction patterns of a double slit, threefold, fourfold and even a fivefold slit, where the slits all have the same widths and the same distance among each other, is to be determined. The intensity relations of the central peaks are to be assessed.
› For transmission grids with different lattice constants, the position of the peaks of several orders of diffraction is to be determined, and the found value used to calculate the wavelength of the laser light.
Slit and double slit systems are illuminated with laser light. The corresponding diffraction patterns are measured by means of a photodiode which can be shifted, as a function of location and intensity.
The experiments that may be carried out with the slits and double slit experimental setup are:
› Determination of the intensity distribution of the diffraction patterns due to two slits of different widths. The corresponding width of the slit is determined by means of the relative positions of intensity values of the extremes. Furthermore, intensity relations of the peaks are evaluated.
› Determination of location and intensity of the extreme values of the diffraction patterns due to two double slits with the same widths, but different distances between the slits. Widths of slits and distances between the slits must be determined as well as the intensity relations of the peaks.
An aperture consisting of a single slit and a complementary strip (wire) is illuminated with a laser beam. The corresponding diffraction patterns are measured according to position and intensity with a photocell which can be shifted.
The experiments that may be carried out with the slit and wire experimental setup are:
› Determination of the intensity distribution of the diffraction patterns due to a slit and complementary strip (wire).
› Determination of the intensity relations of the diffraction pattern peaks for the single slit.
› Babinet’s theorem is discussed using the diffraction patterns of the slit and the complimentary strip.
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experiments >> malu's law
