MCQ
Two coherent sources separated by distance $d$ are radiating in phase having wavelength $\lambda$. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of $n=4$ interference maxima is given as
Image
  • (a) $\sin ^{-1} \frac{n \lambda}{d}$
  • B
    (b) $\cos ^{-1} \frac{4 \lambda}{d}$
  • C
    (c) $\tan ^{-1} \frac{d}{4 \lambda}$
  • D
    (d) $\cos ^{-1} \frac{\lambda}{4 d}$

Answer

Correct option: A.
(a) $\sin ^{-1} \frac{n \lambda}{d}$
(a) $I_0=R^2=\frac{R_2^2}{4}$
Number of $H P Z$ covered by the disc at $b=25 cm$
$n_1 b_1=n_2 b_2 \\n_2=\frac{n_1 b_1}{b_2}+\frac{1 \times 1}{0.25}=4$
Hence the intensity at this point is
$I=R^{\prime 2}=\left(\frac{ R _5}{2}\right)^2$
$=\left(\frac{R_5}{R_4} \times \frac{R_4}{R_3} \times \frac{R_3}{R_2}\right)^2 \times\left(\frac{R_2}{2}\right)^2$ or $1=[0.9]^6$$I_1=0.531 I_0$
Hence the correct answer will be (a).

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A man drops a ball downside from the roof of a tower of height 400 meters. At the same time another ball is thrown upside with a velocity $50 meter / sec$. from the surface of the tower, then they will meet at which height from the surface of the tower
The period of oscillation of a vibration magnetometer depends on which of the following factors where $l$ is the moment of inertia of the magnet about the axis of suspension, $M$ is the magnetic moment of the magnet and $H$ is the external magnetic field
A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1 \mathrm{gm}$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in $\mathrm{gm} / \mathrm{sec}$ will be
Two trains are moving towards each other at speeds of $20 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$ relative to the ground. The first train sounds a whistle of frequency $600 \mathrm{~Hz}$. the frequency of the whistle heard by a passenger in the second train before the train meets is (the speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$ )
The point representing the cut off grid voltage on the mutual characteristic of triode is
Image
A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is
A monoatomic gas of $n$-moles is heated from temperature $T$ to $T$. under two different conditions (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is
Find the resultant of three vectors $\overrightarrow{O A}, \overrightarrow{O B}$ and $\overrightarrow{O C}$ shown in the following figure. Radius of the circle is $R$.
Image
A cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

Image

One $10 V, 60 W$ bulb is to be connected to $100 V$ line. The required induction coil has self inductance of value $(f=50 Hz )$