uperposition theory in Young double slit experiment, Condition of Maxima and Minima and calculation of Fringe width.

In 1801 Thomas Young provided the first experimental evidence for the wave theory of light from double slit interference experiment. Young allowed the sunlight to pass a through a pin hole So on first screen followed by S1 and S2 at some distance on second screen as shown in figure. On the screen he observed few coloured bright and dark bands. To increase the brightness of bands the pin holes S1 and S2 are replaced by narrow slits and to increase the number of fringes sunlight is replaced by monochromatic source. Finally the interference pattern consists of equally spaced bright and dark fringes are obtained.

Explanation of Experiment

Spherical wave came out as the sunlight passes through the pin hole So, (as per Huygen’s wave theory), the radii of these waves increases as they move away from So, when these spherical waves reaches the second screen again spherical waves came out from S1 and S2, these waves move away from S1 and S2 and hence they superimpose on each other. At the point where wave crest (or trough) of one wave fall on the wave crest (trough) of other, the resultant amplitude is maximum (maximum intensity, as I = A2) and where the wave crest of one fall on the wave trough of other, the resultant intensity is minimum. In this way large number of dark and bright bands are formed on screen.

Interference in Wedge Shaped Film (Reflected Rays)

Thin Film Interference A film of thickness from 0.5 to 10 m is a transparent medium of glass, mica, air enclosed between glass, soap film, etc. When the light is made incident on this thin film partial reflection and partial refraction occur from the top surface of the film. The refracted beam travels in the medium and again suffers partial reflection and partial refraction at the bottom surface of the film. In this way several reflected and refracted rays are produces by a single incident ray. As they moves are superimposed on each other and produces interference pattern. Interference in Parallel Film ( Reflected Rays) Consider a thin film of uniform thickness ‘t’ and refractive index bounded between air. Let us consider monochromatic ray AB is made incident on the film, at B part of ray is reflected (R 1 ) and a part is refracted along BC.At C The beam BC again suffer partial reflection and partial refraction, the reflected beam CD moves again suffer partial

Lloyd's’ mirror experiment

Lloyd's mirror This is another method for finding the wavelength of light by the division of wavefront. Light from a slit So falls on a silvered surface at a very small grazing angle of incidence as shown in the diagram (Figure 1). A virtual image of So is formed at S1. Interference occurs between the direct beam from So to the observer (0) and the reflected beam The zeroth fringe will be black because of the phase change due to reflection at the surface. Application An interesting application of this effect may be observed when a helicopter flies above the sea near a radio transmitter. The helicopter will receive two signals: (a) one signal directly from the transmitter and (b) a second signal after reflection from the sea As the helicopter rises the phase difference between the two signals will alter and the helicopter will pass through regions of maxima and minima. Lloyd's mirror Experiment Lloyd’s Mirror is used to produce two-source interference

Thin-Lens Equation:Newtonian Form

In the Newtonian form of the lens equation, the distances from the focal length points to the object and image are used rather than the distances from the lens. Newton used the "extrafocal distances" xo and xi in his formulation of the thin lens equation. It is an equivalent treatment, but the Gaussian form will be used in this resource.

Optics for Optometry

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