Question

In a single slit diffraction experimental set up, the angular width, of the central maximum, changes by (-25%) when the incident wave length (λ = 600 nm) is changed to a new value, say, λ' . It is also observed that while keeping λ = 600 nm, the arrangement is immersed is a transparent liquid of refractive index μ, the change in angular width observed now is the same as that due to a change of λ to its new value λ' . The value of μ is

(1) 1.2

(2) 1.33

(3) 1.4

(4) 1.5

Answer 1

(2) 1.33

Let ω and ω' be the angular widths of central maximum for wave lengths λ and λ' , respectively. Then

When the arrangement, using λ is immersed inside the liquid, the wave length becomes λ' (= λ/μ)

Since change in angular width is the same, λ' = λ'.