Question

For what wavelength would a half wave plate behave as a half wave plate?

(a) 2λ

(b) λ/2

(c) 3λ

(d) Never

The question was asked during an interview.

My query is from Retardation Plates in section Polarisation of Engineering Physics II

Answer 1

Right option is (a) 2λ

Explanation: For a half-wave plate, t = \(\frac{\lambda}{2(\mu_E-\mu_0)}\)

Multiplying numerator and denominator with 2 we get, t = \(\frac{2\lambda}{4(\mu_E-\mu_0)}\)

As we can see, this resembles the expression for thickness of a quarter-wave plate, t = \(\frac{2\lambda}{4(\mu_E-\mu_0)}\). Thus, for λ’ = 2 λ,  a half wave plate would behave as a quarter-wave plate.