Question

The graph below represents the intensity of light plotted for different positions on a screen. The pattern was created by a single frequency of light (wavelength λ) shining through a pair of slits. The peaks represent bright fringes or spots. The valleys represent dark spots. Label each of the following statements as true or false.

A B C DE F GH I Position on Screen

Position C on the screen is two wavelengths further from one slit than the other.

Position A on the screen is two wavelengths further from one slit than the other.

Position D on the screen is a half wavelength further from one slit than the other.

Position E on the screen is the same distance from each slit.

Position C on the screen is 1 wavelength further from one slit than the other.

Answer 1

Waves from one slit and other slit interfere with each other and makes interference pattern on screen.When path difference between the rays comming from each slit is integral multiple of full wavelength $\lambda$ then there will be bright fringe while if path difference is integral multiple of $\frac{\lambda }{2}$ then there will be destructive interference and we get dark fringe.Path difference between any two consecutive bright and dark fringe is $\frac{\lambda }{2}$ while path difference between two consecutive bright and also two consecutive dark fringe is $\lambda$ .

In the graph E is the central bright fringe where rays from slits have zero path difference.

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Now C is the consecutive bright fringe of central bright fringe E ,so path difference will be equal to 1 wavelength. it should be 1 wavelength futher from one slit than the other.So given statement is false.

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A is the second bright fringe to the left of central bright fringe E so it is two wavelength further from one slit than the other.So this statement is true.

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Since D is consecutive dark fringe of central bright fringe so it is half wavelength further from one slit than the other slit.So this statement is true.

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Since E is the central bright fringe so it is at the same distance from both the slits.So this statement is also true.

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Since C is the consecutive bright fringe of central bright fringe E so clearly it is 1 wavelength further from one slit than the other.So this statement is also true.