A double-slit experiment is immersed in a liquid with a refractive index of 1.33. The separation between the slits is 1.0 mm and the distance between the slit and screen is 1.33 m. If slits are illuminated by a parallel beam of light whose wavelength is 6300 Å, then the fringe width will be:
Correct answer: C. 0.63 mm
- A. 6.3 mm
- B. 63 mm
- C. 0.63 mm
- D. None of these
Explanation
When light travels through a medium with a refractive index, its wavelength changes according to the formula λ' = λ / n, where λ' is the new wavelength, λ is the original wavelength, and n is the refractive index. In this case, the new wavelength in the liquid is 6300 Å / 1.33 = 4736.84 Å. Using this adjusted wavelength in the fringe width formula, we get a fringe width of 0.63 mm. Options A and B do not account for the change in wavelength due to the refractive index, leading to incorrect results. Option D is a general 'none of these' choice without providing any calculation.
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Light is studied through reflection, refraction, dispersion, interference, diffraction and polarization, linking ray behavior with its wave nature. Questions may involve mirrors, lenses, optical instruments, refractive index and image formation, while geometrical optics deals with rays and wave optics explains effects such as interference and diffraction.
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