Question:
Two identical coherent sources placed on a diameter of a circle of radius \(R\) at separation \(x\) \((x \ll R)\) symmetrically about the centre of the circle. The sources emit identical wavelength \(\lambda\) each. The number of points on the circle with maximum intensity is \((x = 5\lambda)\)
Two identical coherent sources placed on a diameter of a circle of radius \(R\) at separation \(x\) \((x \ll R)\) symmetrically about the centre of the circle. The sources emit identical wavelength \(\lambda\) each. The number of points on the circle with maximum intensity is \((x = 5\lambda)\)
Show Hint
Count carefully: \(n = 0\) and \(n = \pm5\) each give 2 points (on the diameter axis), while \(|n| = 1,2,3,4\) each give 4 points (symmetric in all four quadrants).
Updated On: Apr 20, 2026
- 20
- 22
- 24
- 26
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Path difference at point \(P\) on the circle: \(\Delta x = x\cos\theta\). For maxima: \(\Delta x = n\lambda\).
Step 2: Detailed Explanation:
\(\cos\theta = n\lambda/x = n/5\). Condition: \(|\cos\theta| \leq 1\). So, \(n = 0, \pm1, \pm2, \pm3, \pm4, \pm5\). \(n = 5\): \(\theta = 0^\circ, 180^\circ\) → 2 points. \(n = -5\): same 2 points. For \(|n| = 1,2,3,4\): each gives 4 points → total = \(4 \times 4 = 16\). \(n = 0\): gives 2 points. Total points: \(2 + 16 + 2 = 20\).
Step 3: Final Answer:
Number of maxima on the circle \(= 20\).
Path difference at point \(P\) on the circle: \(\Delta x = x\cos\theta\). For maxima: \(\Delta x = n\lambda\).
Step 2: Detailed Explanation:
\(\cos\theta = n\lambda/x = n/5\). Condition: \(|\cos\theta| \leq 1\). So, \(n = 0, \pm1, \pm2, \pm3, \pm4, \pm5\). \(n = 5\): \(\theta = 0^\circ, 180^\circ\) → 2 points. \(n = -5\): same 2 points. For \(|n| = 1,2,3,4\): each gives 4 points → total = \(4 \times 4 = 16\). \(n = 0\): gives 2 points. Total points: \(2 + 16 + 2 = 20\).
Step 3: Final Answer:
Number of maxima on the circle \(= 20\).
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET wave interference Questions
- In a Young's double slit experiment, if the distance between the slits is halved and the distance of the screen from the slits is doubled, then the fringe width will:
- Excess of carbon dioxide is passed through 50 mL of 0.5 M calcium hydroxide solution. After the completion of the reaction, the solution was evaporated to dryness. The solid calcium carbonate was completely neutralised with 0.1 N hydrochloric acid. The volume of hydrochloric acid required is (Atomic mass of calcium = 40)
- In Young's double slit experiment, if the source of light changes from orange to blue, then
- A thin film of soap solution (\(\mu_s = 1.4\)) lies on the top of a glass plate (\(\mu_g = 1.5\)). When incident light is almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 420 nm and 630 nm. The minimum thickness of the soap solution is
- Two slits 4 mm apart, are illuminated by light of wavelength 6000 A. What will be the fringe width on a screen placed 2 m from the slits?
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions