A thin film (
)of thickness 77.6 nm,applied to a camera lens (
),is the minimum thickness that results in destructive interference for reflected light of wavelength 450 nm.which of the following is the next greater thickness that will also give destructive interference for this wavelength?
A) 120 nm
B) 155 nm
C) 116 nm
D) 233 nm

Question

A thin film ( 
)of thickness 77.6 nm,applied to a camera lens ( 
),is the minimum thickness that results in destructive interference for reflected light of wavelength 450 nm.which of the following is the next greater thickness that will also give destructive interference for this wavelength?
A) 120 nm 
B) 155 nm 
C) 116 nm 
D) 233 nm

Quizplus · Accepted Answer

For destructive interference to occur, the reflected waves from the two surfaces of the thin film must be out of phase by half a wavelength (λ/2). The condition for this is:

2nt = (m + 1/2)λ

where n is the refractive index of the film, t is the thickness of the film, m is an integer (0,1,2,...) representing the order of the interference fringes.

For the given situation, m = 0 (minimum thickness for destructive interference), λ = 450 nm, and n = 1.5 (assumed for illustration purpose).

2 x 1.5 x 77.6 x 10^-9 m = (0 + 1/2) x 450 x 10^-9 m
=> t = 155.2 nm

Therefore, the next greater thickness that will also give destructive interference for this wavelength is 155 nm, which corresponds to option D.

A Thin Film