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Statement for Linked Answer Questions 54 and 55: A monochromatic plane wave of wavelength λ = 600 nm 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_i are

1. (A) 60° and (E₀)/(√(2)) âₓ â_z e^(-j(10⁴π(x+z))/(3√(2))) V/m
2. (B) 45° and (E₀)/(√(2)) âₓ â_z e^(-j(10⁴π z)/(3)) V/m
3. (C) 45° and (E₀)/(√(2)) âₓ â_z e^(-j(10⁴π(x+z))/(3√(2))) V/m
4. (D) 60° and (E₀)/(√(2)) âₓ â_z e^(-j(10⁴π z)/(3)) V/m

Correct answer: (C) 45° and (E₀)/(√(2)) âₓ â_z e^(-j(10⁴π(x+z))/(3√(2))) V/m

Solution

The correct option indicates an angle of incidence of 45°, which is a common angle for optimal reflection and transmission in wave interactions. The expression for the electric field vector correctly incorporates the propagation direction and the wave's characteristics, including the appropriate phase factor and normalization.

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