SATHEE: Optics 6 Question 31

Optics 6 Question 31

33. Column I shows four situations of standard Young’s double slit arrangement with the screen placed far away from the slits $S_{1}$ and $S_{2}$ . In each of these cases $S_{1} P_{0} = S_{2} P_{0}, S_{1} P_{1} - S_{2} P_{1} = \frac{λ}{4}$ and $S_{1} P_{2} - S_{2} P_{2} = λ / 2$ , where $λ$ is the wavelength of the light used. In the cases $B, C$ and $D$ , a transparent sheet of refractive index $μ$ and thickness $t$ is pasted on slit $S_{2}$ . The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $δ (P)$ and the intensity by $I (P)$ . Match each situation given in Column I with the statement(s) in Column II valid for that situation.

(2009)

Objective Questions II (One or more correct option)

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Solution:

(A) $\to (p, s) \to$ Intensity at $P_{0}$ is maximum. It will continuously decrease from $P_{0}$ towards $P_{2}$

$(B) \to (q) \to$ Path difference due to slap will be compensated by geometrical path difference. Hence, $δ (P_{1}) = 0$ .

(C) $\to (t) \to δ (P_{0}) = \frac{λ}{2}, δ (P_{1}) = \frac{λ}{2} - \frac{λ}{4} = \frac{λ}{4}$ and $δ (P_{2}) = \frac{λ}{2} - \frac{λ}{3} = \frac{λ}{6}$ . When path difference increases from 0 to $\frac{λ}{2}$ , intensity will decrease from maximum to zero. Hence, in this case,

$I (P_{2}) > I (P_{1)} > I (P_{0})$

(D) $\to (r, s, t$ ,

$\begin{aligned} δ (P_{0}) & = \frac{3 λ}{4}, δ (P_{1}) = \frac{3 λ}{4} - \frac{λ}{4} = \frac{λ}{2} \\ and δ (P_{2}) & = \frac{3 λ}{4} - \frac{λ}{3} = \frac{5 λ}{12} . \end{aligned}$

In this case $I (P_{1}) = 0$ .

Optics 6 Question 31

Objective Questions II (One or more correct option)

Solution:

Engineering Preparation

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Optics 6 Question 31

Objective Questions II (One or more correct option)

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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