JEE Physics Wave Optics Notes Set 01

Huygens' Wave Theory

1. Every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the forward envelope of these wavelets. The principle works for all kinds of waves and explains reflection and refraction.
2. The wave theory could not explain polarisation as long as light was assumed longitudinal. Interference, diffraction and polarisation prove the wave nature of light, while the photoelectric effect shows its particle nature.

Interference of Light

1. Two waves interfere when they have the same frequency and a constant phase difference (coherent). Independent sources are incoherent. Coherent beams are produced by division of wavefront (Young's slits) or division of amplitude (thin films).
2. The resultant intensity is \( I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi \). For equal intensities \( I=4I_0\cos^2(\phi/2) \). Phase difference is \( \phi=2\pi\Delta x/\lambda \).
3. Maxima: \( \Delta x=n\lambda \). Minima: \( \Delta x=(2n-1)\lambda/2 \). \( I_{max}/I_{min}=\left(\dfrac{a_1+a_2}{a_1-a_2}\right)^2 \). Energy is only redistributed and the average intensity is \( I_1+I_2 \).

Young's Double Slit Experiment

1. Fringe width is \( \beta=\lambda D/d \). It increases with wavelength and screen distance and decreases with slit separation. In a medium of index \( \mu \) the width becomes \( \beta/\mu \).
2. A thin sheet of thickness t and index \( \mu \) over one slit adds a path \( (\mu-1)t \) and shifts the whole pattern by \( \dfrac{D}{d}(\mu-1)t \), towards the side of the sheet, without changing the fringe width.
3. In white light the central fringe is white and the others are coloured; violet fringes are nearest the centre. Unequal slit widths reduce contrast but do not remove the fringes.
4. Thin films show colours due to interference of reflected light; a very thin film looks black in reflection.

Diffraction

1. Diffraction is the bending of waves around obstacles and is easily seen when the obstacle or slit is comparable to the wavelength. Sound diffracts easily, radio waves more than light.
2. For a single slit of width a, minima occur at \( a\sin\theta=n\lambda \). The central maximum is brightest and has width \( 2\lambda D/a \), twice that of the other fringes. It becomes wider when the slit is made narrower or the wavelength is increased.