- #1
assed
- 27
- 1
Hello. I have been studying interference and diffraction and one doubt has appeared. When you consider the double slit experiment forgeting the effects of diffraction you get the following equation for intensity
[itex]I^{}=4I_{0}cos^{2}(\frac{πdsin(θ)}{λ})[/itex]
where d is the distance between the slits.
For the single slit diffraction we get
[itex]I^{}=I_{0}(\frac{sin(x)}{x})^{2}[/itex]
[itex]x^{}=(\frac{asinθπ}{λ})[/itex]
where a is the width of the slit.
Then for the double-slit case considering diffraction we get
[itex]I^{}=4I_{0}cos^{2}(\frac{πdsin(θ)}{λ})(\frac{sin(x )}{x})^{2}[/itex]
My doubt raises when i consider the two limit cases:
1.For a/λ going to 0 the expression becomes that of the interference-only case.
2.But when we consider d=0(the distance between the centers of the slits) the expression obtained is
[itex]I^{}=4I_{0}(\frac{sin(x)}{x})^{2}[/itex]
which is different from that of the single slit case although doing d=0 we are turning two slits of width a in one slit of width a.
My thoughts trying to solve this problem have considered that maybe I am taking the limit case wrong (although I haven't found where) or some expression for the intensity is wrong.
Thanks in advance for your attention, expecting a good answer...
[itex]I^{}=4I_{0}cos^{2}(\frac{πdsin(θ)}{λ})[/itex]
where d is the distance between the slits.
For the single slit diffraction we get
[itex]I^{}=I_{0}(\frac{sin(x)}{x})^{2}[/itex]
[itex]x^{}=(\frac{asinθπ}{λ})[/itex]
where a is the width of the slit.
Then for the double-slit case considering diffraction we get
[itex]I^{}=4I_{0}cos^{2}(\frac{πdsin(θ)}{λ})(\frac{sin(x )}{x})^{2}[/itex]
My doubt raises when i consider the two limit cases:
1.For a/λ going to 0 the expression becomes that of the interference-only case.
2.But when we consider d=0(the distance between the centers of the slits) the expression obtained is
[itex]I^{}=4I_{0}(\frac{sin(x)}{x})^{2}[/itex]
which is different from that of the single slit case although doing d=0 we are turning two slits of width a in one slit of width a.
My thoughts trying to solve this problem have considered that maybe I am taking the limit case wrong (although I haven't found where) or some expression for the intensity is wrong.
Thanks in advance for your attention, expecting a good answer...