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Correct Answer: 4
1 in the double slit experiment, the fringe pattern observed on a screen is a result of constructive and destructive interference of light waves emanating from two slits. the condition for constructive interference, which leads to bright fringes, can be described by the equation \(d \sin \theta = m \lambda\), where \(d\) is the distance between the slits, \(\theta\) is the angle of incidence at which the maximum occurs, \(m\) is the order of the maximum, and \(\lambda\) is the wavelength of the light used.
2 in this particular problem, we are given that the second order of maximum (\(m = 2\)) occurs at an angle \(\theta = 90^\circ\), and the wavelength of the light (\(\lambda\)) is 2 meters. these values need to be substituted into the interference condition equation to solve for \(d\), the slit separation.
3 by substituting the given values into the formula, we have:
\[
d \sin 90^\circ = 2 \times 2
\]
since \(\sin 90^\circ = 1\), the equation simplifies to:
\[
d \times 1 = 4
\]
thus, \(d = 4\) meters.
4 therefore, the distance between the slits, or the slit separation, is 4 meters. this separation causes the second order bright fringe to appear at an angle of \(90^\circ\) when the light of wavelength 2 meters is used in the experiment.
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