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Question 11 Mark

Plane microwaves are incident on a long slit having a width of 5.0cm. Calculate the wavelength of the microwaves if the first diffraction minimum is formed at $\theta=30^\circ.$

Answer

For first minimum diffraction, $\text{b}\sin\theta=\lambda$Here, $\theta=30^\circ,\text{b}=5\text{cm}$
$\therefore\lambda=5\times\sin30^\circ=\frac{5}{2}=2.5\text{cm}.$

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Question 21 Mark

Find the thickness of a plate which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it normally. The refractive index of the plate is $\mu$.

Answer

Let, t = thickness of the plate Given, optical path difference $=(\mu-1)\text{t}=\frac{\lambda}{2}$$\Rightarrow\text{t}=\frac{\lambda}{2(\mu-1)}$

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Question 31 Mark

Consider the situation of the previous problem. If the mirror reflects only 64% of the light energy falling on it, what will be the ratio of the maximum to the minimum intensity in the interference pattern observed on the screen?

Answer

Given that, the mirror reflects 64% of energy (intensity) of the light.
So, $\frac{\text{I}_1}{\text{I}_2}=0.64=\frac{16}{25}\Rightarrow\frac{\text{r}_1}{\text{r}_2}=\frac{4}{5}$
So, $\frac{\text{I}_\text{max}}{\text{I}_\text{min}}=\frac{(\text{r}_1+\text{r}_2)^2}{(\text{r}_1-\text{r}_2)^2}=81:1.$

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