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Electromagnetic Waves question

2022 · 26 Jun · Shift 1 · Q56
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  5. /2022 · 26 Jun · Shift 1 · Q56

Electromagnetic Waves question

2022 · 26 Jun · Shift 1 · Q56

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size λ100{\lambda \over {100}}100λ​, where λ\lambdaλ is the wavelength of the wave in free space. The phenomenon, which happens there will be :
  1. A
    Reflection
  2. B
    Refraction
  3. C
    Diffraction
  4. D
    Scattering
View written solutionFree

Correct answer: D

  1. Given data
  • Frequency of electromagnetic wave: f=3 GHz=3×109 Hzf = 3\ \text{GHz} = 3 \times 10^9\ \text{Hz}f=3 GHz=3×109 Hz
  • Object size: λ100\dfrac{\lambda}{100}100λ​, where λ\lambdaλ is the wavelength of the wave.
  1. Find the wavelength in free space

For an electromagnetic wave in free space,

λ=cf\lambda = \frac{c}{f}λ=fc​

where c=3×108 m/sc = 3 \times 10^8\ \text{m/s}c=3×108 m/s.

So,

λ=3×1083×109=10−1=0.1 m\lambda = \frac{3 \times 10^8}{3 \times 10^9} = 10^{-1} = 0.1\ \text{m}λ=3×1093×108​=10−1=0.1 m

Thus the object size is

λ100=0.1100=10−3 m\frac{\lambda}{100} = \frac{0.1}{100} = 10^{-3}\ \text{m}100λ​=1000.1​=10−3 m
  1. Compare object size with wavelength

The object size is much smaller than the wavelength:

size=λ100≪λ\text{size} = \frac{\lambda}{100} \ll \lambdasize=100λ​≪λ
  1. Decide the relevant phenomenon
  • Reflection is prominent when the obstacle/surface is large compared to wavelength.
  • Refraction occurs when a wave passes from one medium to another.
  • Diffraction is significant when aperture/obstacle size is comparable to wavelength.
  • Scattering occurs when the obstacle/particle size is much smaller than the wavelength.

Since the object size is λ/100\lambda/100λ/100, i.e. much smaller than the wavelength, the wave will undergo scattering.

  1. Evaluate options
  • A: Reflection →\rightarrow→ Incorrect
  • B: Refraction →\rightarrow→ Incorrect
  • C: Diffraction →\rightarrow→ Incorrect
  • D: Scattering →\rightarrow→ Correct

Therefore, the correct answer is:

D: Scattering\boxed{\text{D: Scattering}}D: Scattering​
  1. Comparison with stored answer

Stored correct answer: D

My derived answer is also D, so they agree.

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