JEE Advanced · Physics · 25. Wave Optics

Paragraph I: In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of \(0.8 \mathrm{~mm}\). The distance between the slits at time \(t\) is given by \(d=(0.8+0.04 \sin \omega t) \mathrm{mm}\), where \(\omega=0.08 \mathrm{rad} \mathrm{s}^{-1}\). The distance of the screen from the slits is \(1 \mathrm{~m}\) and the wavelength of the light used to illuminate the slits is \(6000 Ã…\). The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point \(O\).

The \(8^{\text {th }}\) bright fringe above the point \(\mathrm{O}\) oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer \((\mu \mathrm{m})\), is ___________ .

A 604.5
B 601.5
C 605.7
D 615.8

Verified Solution

Answer & Solution

Correct Answer

(B) 601.5

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & y=n \cdot\left(\frac{\lambda D}{d}\right) \\ & \text { for } 8^{\text {th }} \text { fringe } \\ & y=8 \frac{\lambda D}{d} \\ & y_{\max }=8 \frac{\lambda D}{d_{\min }} \\ & y_{\min }=8 \frac{\lambda D}{d_{\max }} \\ & y_{\max }-y_{\min }=8 \lambda D\left[\frac{1}{d_{\min }}-\frac{1}{d_{\max }}\right] \\ & \lambda=6000 Ã…\end{aligned}\)
\(\mathrm{D}=1 \mathrm{~m} \)
\( \mathrm{~d}_{\max }=0.34 \mathrm{~mm} \)
\( \mathrm{~d}_{\text {min }}=0.76 \mathrm{~mm} \)
\( y_{\max }-y_{\min }=8 \times 6000 \times 10^{-10} \times 1\) \(\left[\frac{1}{0.76 \times 10^{-3}}-\frac{1}{0.84 \times 10^{-3}}\right] \)
\( =8 \times 6 \times 10^{-4} \times\left[\frac{0.08}{0.76 \times 0.84}\right]=601.5 \mu \mathrm{m}\)
(answer range is from 598 to 602 )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List I with List II and select the correct answer using the codes given below the lists:

	\(\text{List I}\)		\(\text{List II}\)
a.	Boltzmann constant	p.	\(\left[M L^2 T^{-1}\right]\)
b.	Coefficient of viscosity	q.	\(\left[M L^{-1} T^{-1}\right]\)
c.	Planck constant	r.	\(\left[M L T^{-3} K^{-1}\right]\)
d.	Thermal conductivity	s.	\(\left[M L^2 T^{-2} K^{-1}\right]\)

JEE Advanced 2013 Easy

Paragraph :
A wooden cylinder of diameter \(4 r\), height \(H\) and density \(\rho / 3\) is kept on a hole of diameter \(2 r\) of a tank, filled with liquid of density \(\rho\) as shown in the figure.

Question :
If height \(h_2\) of water level is further decreased, then

JEE Advanced 2006 Hard

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