In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used as 600 nm. What will be the angular width of the fringe if the entire experiment apparatus is immersed in water? Take refractive index of water to be 4/3.

Solution

Given,
Angular width of a fringe = 0.2^o
Wavelength of light used,

λ

= 600 nm
Refractive index of water,

μ

\frac{4}{3}

Angular fringe separation,

θ = \frac{λ}{d} or d = \frac{λ}{θ}

In water,

d = \frac{λ'}{θ'}

∴

\frac{λ}{θ} = \frac{λ'}{θ'}

\Rightarrow

\frac{θ'}{θ} = \frac{λ'}{λ} = \frac{1}{μ} = 3 / 4

[∵ {}_{a}μ_{ω} = \frac{λ_{α}}{λ_{ω}}]

Angular fringe width when immersed in water,

θ' = \frac{3}{4} θ = \frac{3}{4} \times 0.2 ° = 0.15 ° .

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