Question

A double slit set-up was initially placed in a tank filled with water and the interference pattern was obtained using a laser light. When water is replaced by a transparent liquid of refractive index \( n>n_{\text{water}} \), what will be the effect on the following?
(a) Speed, frequency and wavelength of the light of laser beam.
(b) The fringe width, shape of interference fringes and shift in the position of central maximum.

Hint:

Increasing the refractive index of the medium reduces the wavelength and fringe width of interference patterns, but frequency and central maximum position remain unchanged.

Answer 1

(a) Effect on speed, frequency and wavelength: \begin{itemize}
Speed: Speed of light in a medium is given by \( v = \frac{c}{n} \). Since the refractive index increases, speed decreases.
Frequency: Frequency remains unchanged because it depends only on the source, not on the medium.
Wavelength: Wavelength decreases as \( \lambda = \frac{v}{f} \). With decreased speed and constant frequency, wavelength also decreases. \end{itemize} (b) Effect on interference pattern: \begin{itemize}
Fringe Width: Fringe width \( \beta = \frac{\lambda D}{d} \). As \( \lambda \) decreases in denser medium, fringe width decreases.
Shape of Fringes: The shape remains the same (i.e., still straight and equally spaced), only fringe width changes.
Shift in Central Maximum: There is no shift in the position of the central maximum, as it lies directly opposite the midpoint of the slits. \end{itemize}