A light source simultaneously emits light of two wavelengths, 480 nm and 560 nm, respectively. The source is used in a double-slit interference experiment where the slit spacing is a 0.040 mm, and the distance between double slits and the screen is 1.6 m. What is the separation between the m = 3 bright fringes of the two wavelengths as they appear on the screen? (1 nm = 10 ^- ⁹m)

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Quizplus · Accepted Answer

The separation between the m = 3 bright fringes of the two wavelengths is given by:$$\Delta y = \frac{m\lambda D}{d}$$where:* m is the order of the bright fringe* λ is the wavelength of light* D is the distance between the double slits and the screen* d is the slit spacingFor the 480 nm wavelength, the separation is:$$\Delta y_1 = \frac{3(480 	imes 10^{-9} 	ext{ m})(1.6 	ext{ m})}{0.040 	imes 10^{-3} 	ext{ m}} = 0.0192 	ext{ m} = 1.92 	ext{ cm}$$For the 560 nm wavelength, the separation is:$$\Delta y_2 = \frac{3(560 	imes 10^{-9} 	ext{ m})(1.6 	ext{ m})}{0.040 	imes 10^{-3} 	ext{ m}} = 0.0224 	ext{ m} = 2.24 	ext{ cm}$$The separation between the two bright fringes is:$$\Delta y = \Delta y_2 - \Delta y_1 = 2.24 	ext{ cm} - 1.92 	ext{ cm} = 0.32 	ext{ cm}$$Therefore, the correct answer is A.

A Light Source Simultaneously Emits Light of Two Wavelengths, 480