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In a Lloyd's mirror interference setup, the source plane and screen are 1 m apart. At an initial source position, the fringe width is 1/4 mm. When the source is moved 0.6 mm away from the mirror along the line perpendicular to it, the fringe width changes to 1/6 mm. Identify the correct statement(s):

1. Wavelength of light used is 5000 Angstrom
2. Wavelength of light used is 6000 Angstrom
3. Initial distance of source from the mirror axis is 1.2 mm
4. Initial distance of source from the mirror axis is 0.6 mm

Correct answer: Wavelength of light used is 6000 Angstrom

Solution

Let initial source distance from mirror = d. Fringe width beta = lambda*D/(2d). After moving 0.6 mm farther, new distance = d + 0.6 mm. Using both fringe widths: (1/4)/(1/6) = (d+0.6)/d => 3/2 = (d+0.6)/d => d = 1.2 mm. Then lambda = beta*2d/D = (1/4 * 10⁻³)*2*1.2*10⁻³/1 = 6*10⁻⁷ m = 6000 Angstrom.

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