![]() Using the Fourier Transform (similar to our study of sound and harmonics) we can come up with “optical frequencies.” So the diffraction “pattern” produced by a grating is actually the Fourier Transform of the geometry of that physical grating. The mathematics describing the pattern observed does depend on the geometry of the grating. sin T l / a () note that the width of the central diffraction maximum is inversely proportional to the width of the slit. The light which will be reflected due to constructive interference depends on the wavelength and the thickness of the film (the the index of refraction in the film).Ī diffraction grating is a series of slits which we can use to create a series of spaced out fringes. You can produce the nice colored fringes that you often see on gasoline slicks or soap bubbles. Perhaps the key thing to take away from this equation is that for larger wavelengths the degree of spreading is greater.Īn interesting phenomena called thin film interference happens when light interference with itself by reflecting between surfaces of a film. With one slit you get just the diffraction pattern associated with that slit. With two slits you get diffraction from each slit and also interference of the waves from the two slits. So for small angles we can get away with using one equation for both of these phenomena. It can be useful to distinguish the words 'diffraction' and 'interference'. We can see for the double slit interference, things are similar but not exactly the same We have the latter, but we need to calculate the former. The equation for single slit diffraction can be found at hyperphysics with a nice explanation of the concepts. We can use Equation 3.4.3 for finding the angular deviation from the center line for a single slit, but it requires the wavelength of the wave as well as the slit gap. Where λ is wavelength, d is the slit separation, x is the fringe spacing, and L is the distance to the screen. This angle is important because it is the 2 Diffraction and Interference limit of the angular resolution of an optical system. Your workbook will lead you to believe you can swap the equation between these two related, but different phenomena. However, the equations which describe the location of fringes, or anti-nodes are different, and the physical underpinnings of these equations are different. In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens. Interference and diffraction are different phenomena, although there are significant connection. This is known as Young’s Principle, who first did several experiments with slits, and is well known for observing the interference of slight using a 2 slit experiment. Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0º 45. Λ = 5000 Å = 5000 x 10 -10 m = 5 x 10 -7 mĭ = 0.It appears as if the slit itself is the source of circular waves as opposed to the original source. Monochromatic light with wavelength of 5000 Å (1 Å = 10 −10 m) passes through the single slit, produces diffraction pattern the first maximum as shown in figure. The angle is so small that the sin θ ≈ tan θ.Įquation of d iffraction by a single slit (min ima ) :Ģ. ![]() ![]() The width of the slit is minimal compared to the distance between the slit and the screen so that the angle is minimal (the width of the slit in the figure above is enlarged). Determine the distance between the central maximum and the second minimum. ![]() The diffraction pattern on a screen 60 cm away. Light with wavelength of 500 nm passes through a slit 0.2 mm wide. ![]()
0 Comments
Leave a Reply. |