a) What is the equation that gives the angles of interference maxima for a doubl

Question

a) What is the equation that gives the angles of interference maxima for a double slit setup? Make a sketch that identifies each variable in your equation

b) What is the equation that gives the angles of dark fringes for single slit diffraction? Again, make a sketch that identifies all variables in your equation

c) The expression for the first double-slit maximum("n=1") looks very similar to that for the first single slit minimum. Yet one answer describes a maximum, while the other describes a minimum. how can that be?

Please help!

Explanation / Answer

a)

d sin = m and m=0,±1,±2,±3,....

b)

d sin = (m+1/2) and m=0,±1,±2,±3,....

c)

To analyze the diffraction pattern in a single slit, it is convenient to divide the slit into two
halves, as shown in Figure 38.5. Keeping in mind that all the waves are in phase
as they leave the slit, consider rays 1 and 3. As these two rays travel toward a viewing
screen far to the right of the figure, ray 1 travels farther than ray 3 by an
amount equal to the path difference (a/2) sin , where a is the width of the slit.

If this path difference is exactly half a wavelength (corresponding to a phase difference of
180°), then the two waves cancel each other and destructive interference results.

Therefore

a/2 sin = /2 ===> a sin =

This looks very similar to that for the first single slit minimum.

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