## Related questions with answers

In a Young"s two-slit experinemt a pieve of glass with an index of refraction $n$ and a thickness $L$ is placed in front of the upper slit. (a) Describe qualitatively what happens to the interference pattern. (b) Derive an expression for the intensity $I$ of the light at points on a screen as a function of $n, L$, and $\theta$. Here $\theta$ is the usual angle measured from the center of the two slits. That is, determine the equation analogous to Eq. (35.14) but that also involves $L$ and $n$ for the glass plate. (c) From your result in part (b) derive an expression for the values of $\theta$ that locate the maxima in the interference pattern [that is, derive an equation analogous to Eq.

Solution

Verified$\textbf{a)}$ \ \ If we have value of oil thickness $\lambda = 380 \ \text{nm}$, expression of light wavelenght $\lambda$ is defined as:

$\begin{equation*} \lambda = \frac{\lambda_o}{n} \end{equation*}$

Interference between rays reflected from two surfaces of a thin film will be for constructive reflection from thin film and half-cycle relative phase shift where we insert the expression that consists the wavelenght of light $\lambda_o$ through the oil ($n=1.45$):

$\begin{align*} &2 \cdot t = \left( m + \frac{1}{2} \right) \cdot \lambda \ \ (m=0, 1, 2, ...) \\ \\ &2 \cdot t = \left( m + \frac{1}{2} \right) \cdot \frac{\lambda_o}{n} \\ \\ &\lambda_o = \frac{2 \cdot t \cdot n}{\left( m + \frac{1}{2} \right)} \end{align*}$

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