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Wave Optics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsWave Optics3 Marks
Question
In Young's double$-$slit experiment, interference fringes are observed on a screen $1 m$ away from the two slits which are $2\ mm$ apart. A point $P$ on the screen is $1.8\ mm$ from the central bright fringe,
$(i)$ Find the path difference at $P$.
$(ii)$ If the wavelength of the light used in $4800 A$, what can you say about the illumination at $p?$
✓

Answer

$D =1 m ,$
$d =2\ mm =2 \times 10^3 m ,$
$y =1.8 mm =1.8 \times 10^3 m ,$
$\lambda=4800 A =4.8 \times 10^7$ m
$(i)$ Path differenne $-\frac{z_1^{\prime}}{D}-\frac{\left(1.8 \times 10^{-5}\right)\left(2 \times 10^{-3}\right)}{1}$
$-3.6 \times 10^{-7}$ in 
$(ii) \frac{\text { Path difference }}{2}=\frac{3.5 \times 10^{-6}}{4.8 \times 10^{-7}}-\frac{15}{2}$
$\therefore$ Path differenoe $-15 \frac{2}{2}$
$\therefore$ Path difference $=15 \frac{\lambda}{2}$
As the path difference is an odd integral multiple of $\frac{\lambda}{2}$,
point $P$ is a dark point with minimum intensity.

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