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Question:

Answer the following questions: (a) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits. (b) Light of wavelength 5000 Å propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

Solution:

(a) The width of the fringe on the screen is given by β = λD/d. The angular width is thus given by λ/d = 0.1° => d = 600 × 10⁻⁹ / (0.1 × π/180) = 0.344 mm
(b) Frequency of the reflected and refracted lights remains the same. As the velocity of light decreases in water, which implies wavelength decreases in water. Thus, the refracted light has a lower wavelength than the reflected light.