Laws of reflection on the basis of Huygen’s Wave Theory

In the given figure, AB is the wavefront incident on a reflecting surface XY with an angle of incidence i as shown in figure. According to Huygen’s principle, every point on AB acts as a source of secondary wavelets. At first, wave incidents at point A and then to points C, D and E. They form a sphere of radii AA1, CC1 and DD1 as shown in figure.

A1E represents the tangential envelop of secondary wavelet in forward direction.

In ΔABE and ΔAA1E,

∠ABE = ∠AA1E = 90°

Side AE = Side AE

AA1 = BE = distance travelled by wave in same time

So, these triangles are congruent.

So, ∠BAE = i and ∠BEA =r

Thus, i = r

Hence, angle of incidence is equal to the angle of reflection. This is the first law of reflection.

Since, the incident wavefront AB, normal and reflected wavefront A1E lies in same plane, it verifies the second law of reflection.

In this way, laws of reflection is verified by Huygens’s principle.

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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