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Wave Optics Quiz 8

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JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts. .

Q1. The index of refraction of a glass plate is 1.48 at 𝜃1 = 30°C and varies linearly with temperature with a coefficient of 2.5 × 10-5°C-1. The coefficient of linear expansion of the glass is 5 × 10-5°C-1. At 30°C, the length of the glass plate is 3 cm. This plate is placed in front of one of the slits in Young’s double-slit experiment. If the plate is being heated so that its temperature incraeses at a rate of 5°C-1 min, the light source has wavelength 𝜆 = 589 nm and the glass plate initially is at 𝜃 = 30°C. The number of fringes that shift on the screen in each minute is nearly (use approximation)
  •  Frequency v and wavelength 1
  •  Frequency v and wavelength 11
  •  110
  •  1.1×103
Solution

Q2.In a two-slit experiment with white light, a white fringe is observed on a screen kept behind the slits. When the screen in moved away by 0.05 m, this white fringe
  •  Does not move at all
  •  Gets displaced from its earlier position
  •  Becomes coloured
  •  Disappears
Solution
Q3.  Two identical coherent sources of wavelength 𝜆 are placed at (100𝜆, 0) and (−50𝜆, 0), respectively. A detector moves slowly from the origin to (50𝜆, 0) along 𝑥-axis. The number of maxima and minima detected are, respectively [include origin and (50𝜆, 0)]
  •   51 and 50
  •  101 and 100
  •  49 and 50
  •  50 and 49
Solution

Q4. Young’s double-slit experiment is made in a liquid. The 10th bright fringe in liquid lies where 6th dark fringe lies in vacuum. The refractive index of the liquid is approximately
  •  1.8
  •  1.54
  •  1.67
  •  1.2
Solution

Q5.Two transparent slabs have the same thickness as shown in figure. One is made of material 𝐴 of refractive index 1.5. The other is made of two materials 𝐵 and 𝐶 with thickness in the ratio 1:2. The refractive index of 𝐶 is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both, the refractive index of 𝐵 is
  •  1.1
  •  1.2
  •  1.3
  •  1.4
Solution

Q6. In a Young’s double-slit experiment, the separation between the slits is 𝑑, distance between the slit and screen is 𝐷(𝐷 ≫ 𝑑). In the interference pattern, there is a maxima exactly in front of each slit. Then, the possible wavelength(s) used in the experiment are
  •  ð‘‘2/𝐷, 𝑑2/2𝐷, 𝑑2/3𝐷
  •  ð‘‘2/𝐷, 𝑑2/3𝑑, 𝑑2/5𝐷
  • 𝑑2/2𝐷, 𝑑2/4𝐷, 𝑑2/6𝐷
  •  None of these
Solution
Q7.A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for 𝜆 = 5000 Å and λ = 1000 Å and for no other wavelength in between. If 𝜇 of oil is 1.3 and that of glass is 1.5, the thickness of the film will be
  •  6.738×10-5cm
  •  5.7×10-5cm
  •  4×10-5cm
  •  2.8×10-5cm
Solution
Q8.Consider an YDSE that has different slit widths. As a result, amplitude of waves from two slits are 𝐴 and2𝐴, respectively. If 𝐼0 be the maximum intensity of the interference pattern, then intensity of the pattern at a point where phase difference between waves is 𝜙 is
  •  ð¼0cos2𝜙
  •  
    𝐼0 / 3
    sin2
    𝜙 / 2
  •  
    𝐼0 / 8
    [5+4cos𝜙]
  •  
    𝐼0 / 8
    [5+8cos𝜙]
Solution
Q9.In a standard Young’s double-slit experiment with coherent light of wavelength 600 nm, the fringe width of the fringes in the central region (near the central fringe, 𝑃0) is observed to be 3 mm. An extremely thin 0 glass plate is introduced in front of the first slit, and the fringes are observed to be displaced by 11 mm. Another thin plate is placed before the second slit and it is observed that the fringes are now displaced by and additional 12 mm. If the additional optical path lengths introduced are ∆1 and ∆2, then
  •  11∆1=12∆2
  •  12∆1=11∆2
  •  11∆1>12∆2
  •  None of the above
Solution
Q10. In YDSE, having slits of equal width, let 𝛽 be the fringe width and 𝐼0 be the maximum intensity. At a distance 𝑥 from the central bright fringe, the intensity will be
  •  ð¼0cos(
    x / 𝛽
    )
  •  ð¼0cos2
    2𝜋x / 𝛽
  •  ð¼0cos2
    𝜋x / 𝛽
  • 𝐼0 / 4
    cos2
    𝜋x / 𝛽
Solution

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