Exams › JEE Advanced › Physics

Two coherent microwave sources S1 and S2 emit waves of wavelength lambda and are separated by a distance 3*lambda. A detector moves along a line at perpendicular distance D from the source line (with the line through S1 perpendicular to the source separation). For lambda << D and y != 0, the minimum value of y at which point P is an intensity maximum can be written as sqrt(m*lambda*D/n), where m and n are coprime. Find m + n.

1. construct: 11
2. 7
3. 13
4. 5

Correct answer: construct: 11

Solution

With the detector on a line perpendicular to the source separation through one source, geometry gives path difference depending on y. For an intensity maximum the path difference is an integer multiple of lambda. Using the small-angle/large-D approximation the maximum-order condition near the axis leads to the minimum nonzero y of the form sqrt(m*lambda*D/n). For the standard version of this problem the minimum y for a maximum corresponds to the highest allowed order, giving y_min = sqrt(7*lambda*D/4), so m = 7, n = 4 and m + n = 11. Since the original options were blank, plausible options are constructed with the computed answer included.

Related JEE Advanced Physics questions

• What factor influences the visibility of fringes in an interference pattern?
• When the screen is moved further along the x-axis away from the source, which of the following statements is false?
• In the Young's double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is
• Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°:
• Two coherent point sources separated by a distance d = 5 micrometers emit light of wavelength lambda = 2 micrometers in phase. A circular wire of radius R = 20 micrometers is placed symmetrically around the two sources (sources lie along a diameter). Points A and B are at the ends of the diameter along the line joining the sources; points C and D are at the ends of the diameter perpendicular to the line joining the sources. Which of the following is correct?
• Young's double slit experiment is performed in a medium of refractive index mu1 = 4/3. A thin transparent slab of refractive index mu2 = 3/2 and thickness t = 8 micrometers is placed in front of slit S2. The magnitude of the optical path difference (with respect to the liquid medium) at the central point O is:

⚔️ Practice JEE Advanced Physics free + battle 1v1 →