6300 mathring A wavelength light shines on tw | vedclass

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(A) The path difference introduced by a glass plate of thickness $t$ and refractive index $\mu$ is $\Delta x = (\mu - 1)t$.In a Young's Double Slit Ex

Vedclass · Accepted Answer

$1.6$

Vedclass · Answer

(A) The path difference introduced by a glass plate of thickness $t$ and refractive index $\mu$ is $\Delta x = (\mu - 1)t$.In a Young's Double Slit Experiment $(YDSE)$,the shift in the central maxima is given by $\Delta x = d \sin 	heta \approx d 	heta$ (for small $	heta$).When both slits are covered by plates of refractive indices $\mu_1 = 1.8$ and $\mu_2 = \mu$ with the same thickness $t = 0.5 \ mm$,the net path difference is $\Delta x = (\mu_1 - 1)t - (\mu_2 - 1)t = (\mu_1 - \mu_2)t$.Given the shift $	heta = 6^o = 6 	imes \frac{\pi}{180} = \frac{\pi}{30} 	ext{ radians}$.Using the relation $d 	heta = (\mu_1 - \mu_2)t$,we have $\mu_1 - \mu_2 = \frac{d 	heta}{t}$.Substituting the values: $1.8 - \mu = \frac{1.0 	imes 10^{-3} 	imes (\pi/30)}{0.5 	imes 10^{-3}} = 2 	imes \frac{\pi}{30} = \frac{\pi}{15} \approx 0.209$.Thus,$\mu = 1.8 - 0.209 = 1.591 \approx 1.6$.

Similar Questions

To make the central fringe at the centre $O$,a mica sheet of refractive index $1.5$ is introduced. Choose the correct statement$(s)$.

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