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) Impact on Speed, Frequency, and Wavelength:

• Speed: The speed of light in a medium is defined as \( v = \frac{c}{n} \). An increase in the refractive index (n) leads to a decrease in speed (v).
• Frequency: The frequency remains constant, as it is solely determined by the light source and is independent of the medium.
• Wavelength: The wavelength decreases because \( \lambda = \frac{v}{f} \). With a reduced speed (v) and a constant frequency (f), the wavelength (λ) also decreases.

(b) Impact on Interference Pattern:

• Fringe Width: The fringe width is given by \( \beta = \frac{\lambda D}{d} \). A decrease in wavelength (λ) in a denser medium results in a decrease in fringe width (β).
• Shape of Fringes: The shape of the fringes remains unchanged (straight and equally spaced); only the fringe width is altered.
• Shift in Central Maximum: The position of the central maximum does not shift, as it is located directly opposite the midpoint of the slits.