91Ó°ÊÓ

The concept of optical path difference is crucial in understanding the interaction of light through different media. It helps us measure the additional distance that light travels in a medium other than vacuum. To calculate this, use the formula:

• Optical Path Difference = (Refractive Index - 1) * Thickness

In our case, the refractive index (\(\mu\)) of the glass sheet is 1.5, and its thickness is 6 microns. By substituting these values into the formula, we get:\[\text{Optical Path Difference} = (1.5 - 1) \times 6 \text{ microns} = 3 \text{ microns}\]This difference is responsible for shifting the interference pattern in a double slit experiment.

Fringe shift is a key outcome in interference experiments like the double slit experiment. It refers to the movement of interference fringes when an optical path difference is introduced.In this scenario, the introduction of the glass causes a central fringe shift to where the fifth bright fringe would normally appear. This indicates that the glass has induced a path difference equal to the wave path of five wavelengths. We express this as:\[\text{Optical Path Difference} = 5\lambda\]Substituting the previously calculated optical path difference of 3 microns into this equation gives us a framework to solve for the wavelength \(\lambda\), as the fringe shift shows a direct link between path difference and wavelength.

Understanding wavelength in microns helps us handle calculations in a scale appropriate for the phenomenon. In the given problem, the optical path differences and shifts are expressed in microns because the thickness and the light effects involved are minuscule.To find the wavelength \(\lambda\) of the light, we utilize the relationship established from the fringe shift:\[3 \text{ microns} = 5\lambda\]Solving for \(\lambda\), we divide both sides by 5:\[\lambda = \frac{3 \text{ microns}}{5} = 0.6 \text{ microns}\]This calculation gives us the wavelength expressed in microns, a widespread unit choice for physics problems involving light on such small scales.

Converting wavelength from microns to Angstroms is often helpful for scientific applications, where precision and standard units are important. The conversion can be done using the fact that:

• 1 micron = 10,000 Angstroms

In the problem, we determined the wavelength as 0.6 microns, which needs to be converted to Angstroms:\[\lambda = 0.6 \text{ microns} \times 10,000 \text{ Angstroms/micron}\]This results in:\[\lambda = 6000 \text{ Angstroms}\]Thus the wavelength of light in the double slit experiment is 6000 Angstroms, fitting neatly into the unit system used for precise and uniform exchange of scientific information.