Two slits are separated by 2.00 × 10^-⁵ m. They are illuminated by light of wavelength 5.60 × 10^-⁷m. If the distance from the slits to the screen is 6.00 m, what is the separation between the central bright fringe and the third dark fringe? A)0.421 m B)0.224 m C)0.168 m D)0.084 m E)0.070 m

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Quizplus · Accepted Answer

The separation between the central bright fringe and the third dark fringe is given by:$$d\sin	heta=3\lambda$$where d is the separation between the slits, $	heta$ is the angle of the third dark fringe, and $\lambda$ is the wavelength of the light.We can use the small angle approximation to get:$$	an	heta=\frac{y}{L}$$where y is the distance from the central bright fringe to the third dark fringe and L is the distance from the slits to the screen.Substituting this into the first equation, we get:$$d\frac{y}{L}=3\lambda$$Solving for y, we get:$$y=\frac{3\lambda L}{d}$$Plugging in the given values, we get:$$y=\frac{3(5.60	imes10^{-7}	ext{ m})(6.00	ext{ m})}{2.00	imes10^{-5}	ext{ m}}=0.504	ext{ m}$$Therefore, the separation between the central bright fringe and the third dark fringe is 0.504 m.

Two Slits Are Separated by 2