Suppose you illuminate two thin slits by monochromatic...

Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at $\pm 35.20^{\circ}$ on either side of the central bright spot. You then immerse these slits in a transparent liquid and illuminate them with the same light. Now you find that the first minima occur at $\pm 19.46^{\circ}$ instead. What is the index of refraction of this liquid?

Key Concepts

Angular Position of Minima

The angular position of interference minima is determined by the phase difference between the light waves arriving from separate slits. Typically, the condition for the first minimum is expressed in terms of the sine of the angle, wavelength, and the spacing between slits. When the medium is changed, the reduction in wavelength leads to a change in the angle at which the minima occur, revealing the value of the refractive index.

Refractive Index

The refractive index is a measure of how much the speed of light is reduced inside a medium compared to vacuum. It is defined by the ratio of the speed of light in vacuum to that in the material. In interference experiments, changes in the refractive index directly influence the effective wavelength of light, and consequently the position of interference fringes.

Interference Pattern

Interference patterns are formed when two or more coherent light waves overlap and interact, resulting in regions of constructive and destructive interference. The positions of the minima and maxima depend on the wavelength of the light and the geometry of the setup. In typical experiments, the angular positions of the interference minima are used to extract information about the light’s wavelength.

Wavelength Change in a Medium

When light enters a medium other than vacuum or air, its speed decreases while its frequency remains constant. This results in a shorter wavelength, which is given by the relationship ?_medium = ?_air/n, where n is the refractive index of the medium. This change in wavelength affects the interference pattern, shifting the angular positions of the minima and maxima.

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