A linearly polarized electromagnetic wave in vacuum is
E = 3.1 cos [ (1.8)z - (5.4 × 10⁶)t ]îN/C
is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

Solution

Physics sir · 3 steps

Read k and ω off the cosine, then flip the direction of travel for the reflected wave.

1. Read the wave. Compare with E = E₀ cos(kz - ω t). Here E₀ = 3.1 N/C, k = 1.8 rad m⁻¹ and ω = 5.4 × 10⁶ rad s⁻¹. The minus sign means the wave travels along +z.
2. Perfect reflection. A perfectly reflecting wall sends all the energy back, so nothing is transmitted and the amplitude stays 3.1. The reflected wave keeps the same k and ω but travels along -z, so the sign between kz and ω t becomes plus. The options leave out any constant phase set by the wall's position.

   Option	Check	Verdict
   (a) λ = 5.4 m	λ = 2π/k = 2π/1.8 ≈ 3.49 m	wrong
   (b) f = 54 × 10⁴ Hz	f = ω/2π = (5.4 × 10⁶)/2π ≈ 8.6 × 10⁵ Hz	wrong
   (c) transmitted wave	a perfect reflector transmits nothing	wrong
   (d) reflected wave	same amplitude, same k and ω, sign changed to + for travel along -z	correct

3. So. The reflected wave is 3.1 cos[(1.8)z + (5.4 × 10⁶)t]î N/C, which is option (d).

The idea to keep. In cos(kz ∓ ω t), the sign tells you the direction: minus means +z, plus means -z. Reflection reverses that sign and keeps k and ω. Take λ from 2π/k and f from ω/2π.

Answer from the NTA final answer key. Solution by PrepWiser.