When the medium in Young's double slit experiment is replaced by an optically denser medium, the interference pattern changes due to the decrease in the wavelength of light.
Key Changes:
1. Wavelength Decrease:
- The speed of light \(v\) in a medium is given by:
\[ v = \frac{c}{n} \]
where \(c\) is the speed of light in a vacuum and \(n\) is the refractive index of the medium.
- The wavelength \(\lambda\) in the medium is:
\[ \lambda = \frac{\lambda_0}{n} \]
where \(\lambda_0\) is the wavelength in a vacuum.
2. Fringe Width Decrease:
- The fringe width \(w\) is given by:
\[ w = \frac{\lambda D}{d} \]
where \(\lambda\) is the wavelength in the medium, \(D\) is the distance between the slits and the screen, and \(d\) is the distance between the slits.
- In an optically denser medium, since \(\lambda\) decreases, \(w\) also decreases, causing the fringes to be closer together.
3. More Fringes:
- As the fringe width \(w\) decreases, more fringes fit into the same distance on the screen.
Summary:
- Wavelength decreases: \(\lambda = \frac{\lambda_0}{n}\)
- Fringe width decreases: \( w = \frac{\lambda D}{d} \)
- Number of fringes increases.
