A wedge of air between two glass plates is illuminated with 500 nm light.How much thicker (in nm)is the wedge at the 16th dark fringe than it is at the 6th?

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Quizplus · Accepted Answer

The thickness difference between two dark fringes in a wedge-shaped film can be calculated using the formula for the path difference, which is $2t = (m + \frac{1}{2})\lambda$, where $t$ is the thickness at a particular point, $m$ is the order of the fringe (an integer), and $\lambda$ is the wavelength of the light. The difference in thickness ($\Delta t$) between the 16th and 6th dark fringes can be found by calculating the thickness at these points and subtracting one from the other.For the 16th dark fringe ($m = 15$), $2t_{16} = (15 + \frac{1}{2})\lambda = 15.5\lambda$.For the 6th dark fringe ($m = 5$), $2t_{6} = (5 + \frac{1}{2})\lambda = 5.5\lambda$.The difference in thickness is $2\Delta t = 15.5\lambda - 5.5\lambda = 10\lambda$.Given $\lambda = 500$ nm, $2\Delta t = 10 \times 500$ nm = 5000 nm.Since $2\Delta t = 5000$ nm, $\Delta t = 2500$ nm.

A Wedge of Air Between Two Glass Plates Is Illuminated