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Statement for Linked Answer Questions 54 and 55: A monochromatic plane wave of wavelength λ = 600 μm is propagating in the direction as shown in the figure below. E_i, E_r and Eₜ denote incident, reflected, and transmitted electric field vectors associated with the wave. Q.54 The angle of incidence θ_i and the expression for E_r are

1. (A) 60° and E₀/√2 âₓ â_z e^(-j10⁴π(x+z)/(3√2)) V/m
2. (B) 45° and E₀/√2 âₓ â_z e^(-j10⁴π(x+z)/3) V/m
3. (C) 45° and E₀/√2 âₓ â_z e^(-j10⁴π(x+z)/(3√2)) V/m
4. (D) 60° and E₀/√2 âₓ â_z e^(-j10⁴π(x+z)/3) V/m

Correct answer: (C) 45° and E₀/√2 âₓ â_z e^(-j10⁴π(x+z)/(3√2)) V/m

Solution

The correct option indicates that the angle of incidence is 45°, which is a common angle for optimal reflection and transmission conditions in wave interactions. Additionally, the expression for the reflected electric field vector correctly incorporates the wavelength and phase shift, aligning with the properties of wave behavior at this angle.

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