Physics

Physics

Problem

State the expression for the new fringe width when a Young’s double-slit arrangement, which shows a fringe width β\beta in air, is completely immersed in a liquid of refractive index μ\mu; express the answer in terms of β\beta and μ\mu.
Intuitive explanation

The key insight is that immersing the apparatus in a liquid changes the effective wavelength of light without changing the geometry. Since fringe width depends directly on wavelength (β∝λ\beta \propto \lambda), and light travels slower in a medium with refractive index μ\mu, its wavelength shrinks by a factor of μ\mu. You just need to scale the original fringe width accordingly.

Intuitive explanation

The key insight is that immersing the apparatus in a liquid changes the effective wavelength of light without changing the geometry. Since fringe width depends directly on wavelength (β∝λ\beta \propto \lambda), and light travels slower in a medium with refractive index μ\mu, its wavelength shrinks by a factor of μ\mu. You just need to scale the original fringe width accordingly.

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