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Electromagnetic Waves question

2019 · 12 Jan · Shift 1 · Q62
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Electromagnetic Waves question

2019 · 12 Jan · Shift 1 · Q62

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be :
  1. A
    6 V/m
  2. B
    10 V/m
  3. C
    30 V/m
  4. D
    24 V/m
View written solutionFree

Correct answer: D

  1. Given data

    • Refractive index of glass: n=1.5n=1.5n=1.5
    • Reflected light intensity fraction: R=4%=0.04R=4\%=0.04R=4%=0.04
    • Incident electric field amplitude: Ei=30 V/mE_i=30\,\text{V/m}Ei​=30V/m
  2. Relate intensity and electric field amplitude

    For an electromagnetic wave, intensity is proportional to the square of the electric field amplitude: I∝E2I \propto E^2I∝E2

    Hence, if 4%4\%4% of the light is reflected, then the reflected field amplitude satisfies IrIi=(ErEi)2=0.04\frac{I_r}{I_i}=\left(\frac{E_r}{E_i}\right)^2=0.04Ii​Ir​​=(Ei​Er​​)2=0.04

    Therefore, ErEi=0.04=0.2\frac{E_r}{E_i}=\sqrt{0.04}=0.2Ei​Er​​=0.04​=0.2 Er=0.2×30=6 V/mE_r=0.2\times 30=6\,\text{V/m}Er​=0.2×30=6V/m

  3. Use boundary condition for normal incidence

    At the boundary, the tangential component of electric field is continuous, so Ei+Er=EtE_i+E_r=E_tEi​+Er​=Et​ where EtE_tEt​ is the transmitted electric field amplitude in glass.

    Thus, Et=30+(−6)E_t=30+(-6)Et​=30+(−6)

    Since reflection from a denser medium introduces a phase change of π\piπ, the reflected electric field is opposite in sign. So effectively, Et=30−6=24 V/mE_t=30-6=24\,\text{V/m}Et​=30−6=24V/m

  4. Final answer Et=24 V/mE_t=24\,\text{V/m}Et​=24V/m

  5. Option check

    • A: 6 V/m6\,\text{V/m}6V/m →\rightarrow→ reflected amplitude, not transmitted
    • B: 10 V/m10\,\text{V/m}10V/m →\rightarrow→ incorrect
    • C: 30 V/m30\,\text{V/m}30V/m →\rightarrow→ incorrect
    • D: 24 V/m24\,\text{V/m}24V/m →\rightarrow→ correct

Therefore, the amplitude of the electric field in the glass medium is 24 V/m24\,\text{V/m}24V/m.

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