## Wave Optics

# Interference of Light Waves and Young’s Experiment

- Fringe width is the distance between any two consecutive maxima or minima
- Fringe width \tt \beta=\frac{\lambda D}{d}
- Fringe width is independent of the order of fringe.
- Fringe width depends on wave length (λ) of light used.
- Fringe width Depends upon distances between the slits and screen, Distance between slits.
- Fringe width in a medium of refraction index μ \tt \beta'=\frac{\lambda D}{\mu d}
- Angular fringe width \tt \theta=\tan\theta=\frac{\beta}{D}=\frac{\lambda}{d}
- In YDST N
_{1}fringes are visible with light of wavelength λ_{1}and N_{2}fringes with λ_{2 , }N_{1}λ_{1}= N_{2}λ_{2 .} - Number of fringes and fringe width are related as N
_{1}β_{1}= N_{2}β_{2 } - Fringe visibility \tt V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{2\sqrt{I_{1}I_{2}}}{\left(I_{1}+I_{2}\right)}
- If I
_{min}= 0 Then v = 1 maximum visibility. - If I
_{max}= I_{min}then v = 0 bright and does fringes are not distinguishable. - When a transparent plate of thickness ‘t’ and refractive index ‘μ’ in introduced in the path of one of the beams then shift = \tt \frac{D}{d}\left(\mu-1\right)t=\frac{\beta}{\lambda}\left(\mu-1\right)t
- The Effective path in air is increased by an amount (μ − 1)t
- The Shift of fringes is independent of the order of fringe.
- Condition for maxima in interference in thin films \tt 2\ \mu t \cos r=\left(2n-1\right)\frac{\lambda}{2}
- Condition for minima in interference in thin films 2μt cosr = nλ
- Diffraction is the process of bending of light around the corners of obstacle.

### View the Topic in this video From 00:15 To 3:45

### Young's Experiment View the Topic in this video From 00:15 To 20:30

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1. The fringe width β, both for bright and dark fringes is given by

\beta = \frac{D}{d}\lambda

2. Intensity of Fringes :

I = 4I_{0} \cos^{2}\frac{\delta}{2}

3. Eringe visibility \tt V = \left[\frac{I_{max} + I_{min}}{I_{max} - I_{min}}\right]