Y and Z are two partially reflecting glass sheets, a distance $$l$$​ apart in air. White light falls normally on Y. The light emerging from Z is analysed by a spectrometer. A dark band is observed in the spectrometer at a wavelength. The distance $$l$$​ must be equal to:

Correct option is B

When light undergoes interference due to partially reflecting surfaces, dark fringes are observed when destructive interference occurs. The path difference (Δ) for destructive interference is given by the equation:

Δ = (2l + 1)λ/2

Where l is the distance between the two surfaces, and λ is the wavelength of the light.

For destructive interference to occur, the path difference must be an odd multiple of λ/2. Hence, the path difference formula is given as:

Δ = (2n + 1) λ/2, where n = 0, 1, 2, ...

So, the distance 'l' must be equal to:

l = (n + 1/2) λ/2.