Question 48: Wave Optics

Question

A plastic sheet (refractive index = 1 6. ) covers one
slit of a double slit arrangement for the Young’s
experiment. When the double slit is illuminated
by monochromatic light (wavelength = 5867 $$\mathop A\limits^o $$),
the centre of the screen appears dark rather
than bright. The minimum thickness of the
plastic sheet to be used for this to happen is

Accepted Answer

Given, wavelength of monochromatic light, $$\lambda = 5867$$ $$\mathop A\limits^o $$
Refractive index, $$\alpha$$ = $$1.6$$
Let t be the thickness of the plastic.
Since, the centre of the screen appears dark when plastic sheet is introduced, hence path difference,
$$ \alpha t = {\lambda  \over 2}$$ or $${{3\lambda } \over 2}$$
when, $$ \alpha t = {{3\lambda } \over 2}$$
$$ \Rightarrow t = {{3\lambda } \over {2 \alpha }} = {{3 	imes 5867} \over {2 	imes 1.6}} = 5500\mathop A\limits^o $$

Answer

3300 $$\mathop A\limits^o $$

Answer

6600 $$\mathop A\limits^o $$

Answer

2062 $$\mathop A\limits^o $$

Answer

5500 $$\mathop A\limits^o $$

Wave Optics

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