Lloyd's Mirror Experiment

The Lloyd's Mirror Experiment is a classic demonstration of the wave nature of light, where interference patterns are created by reflecting a coherent light source off a mirror to combine with the direct light path. This setup generates alternating bright and dark fringes, illustrating the principles of constructive and destructive interference. This experiment is foundational in understanding optical phenomena and wave behaviour. In real life, the principles from Lloyd's Mirror are applied in various fields, such as in the design of optical instruments, enhancing the precision of interferometric measurements, and even in the development of advanced imaging technologies used in scientific research and medical diagnostics. In this article, we will discuss the concept of Lloyd's mirror experiment with all setup and solved examples related to it.

Lloyd's Mirror Experiment

Lloyd's Mirror Experiment vividly demonstrates the wave nature of light through the phenomenon of interference. By reflecting a coherent light source of a mirror, the experiment creates an interference pattern that can be observed as a series of bright and dark fringes on a screen. These fringes result from the combination of direct light from the source and light that has been reflected off the mirror, highlighting the principles of constructive and destructive interference.

In Lloyd's mirror experiment, light from a monochromatic slit source reflects from a glass surface at a small angle and appears to come from a virtual source as a result. The reflected light interferes with the direct light from the source, forming interference fringes.

Experimental Setup

A plane glass plate (acting as a mirror) is illuminated at almost grazing incidence by a light from a spiritual image $S_2$ of $S_1$ is formed close to $S_1$ by reflection and these two act as coherent sources. The expression giving the fringe width is the same as for the double silt, but the fringe system differs in one important respect.

The path difference $S_2 P-S_1 P$ is a whole number of wavelengths, the fringe at P is dark, not bright. This is due to $180^{\circ}$ phase change which occurs when light is reflected from a denser medium. At grazing incidence, a fringe is formed at O, where the geometrical path difference between the direct and reflected waves is zero and it follows that it will be dark rather than bright.

Thus, whenever there exists a phase difference a $\pi$ between the two interfering beams of light, conditions of maxims and minimus are interchanged, i.e.

$\Delta x=n \lambda$ (for minimum intensity) and

$\Delta x=(2 n-1) \lambda / 2$ (for maximum intensity)

Recommended Topic Video

Solved Example Based on Lloyd's Mirror Experiment

Example : A long narrow horizontal silt is placed 1mm above the horizontal plane mirror the interference between the light coming directly from the silt and that after reflection is seen on a screen 1m away from the silt if $\lambda=700 \mathrm{~nm}$ then fringe width is :

1)20mm

2)25mm

3)30mm

4)35mm

Solution:

Lloyd's Mirror Experiment

for minima $S_2 P-S_1 P=n \lambda$

for maxima $S_2 P-S_1 P=(n+1 / 2) \lambda$

$\begin{gathered}\beta=\frac{\lambda D}{d}=\frac{700 \mathrm{~nm} * 1}{2 \mathrm{~mm}} \\ =35 \mathrm{~mm}\end{gathered}$

Hence, the answer is the option (2).

Summary

The Lloyd's Mirror Experiment demonstrates the wave nature of light by creating interference patterns through the reflection of a coherent light source of a mirror. This setup produces alternating bright and dark fringes due to constructive and destructive interference. The principles of this experiment are foundational in optical science and have practical applications in designing optical instruments, improving interferometric measurements, and developing advanced imaging technologies used in scientific research and medical diagnostics. Through detailed examples, the experiment's concepts and practical implications are clearly illustrated.