Monochromatic light of wavelength 500 nm is used in Young's double… | JEE Main 2024 (9 Apr, Shift 2)

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YDSE: Film, Medium & Two Wavelengths

Monochromatic light of wavelength $500\text{ nm}$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$ ), the central maximum is shifted to a position previously occupied by the $4$ th bright fringe. The thickness of the glass-plate is __________ $\mu\text{m}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 4

Shift to 4th bright fringe: $(\mu - 1)t = 4\lambda$ .
$t = \dfrac{4 \times 500\text{ nm}}{0.5} = 4000\text{ nm}$
So the thickness is $4\ \mu\text{m}$ .

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