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Babinet's Principle

Module by: Paul Padley. E-mail the author

Summary: We discuss Babinet's principle and give an example.

Babinet's Principle

Say you have a slit with light passing through it. You will get a diffraction pattern, lets call it E s E s . If you cover the slit with a piece of material that fits just inside the slit, then there is no E E field in the Fraunhofer limit. The is means that the E E field of the blocker, lets call it v e c E b v e c E b , must exactly cancel E s E s . The only way this can happen is if E b = E s E b = E s . Now if you take the slit away the E E field of the blocker must still remain and then irradiance must be I b = ( E s ) 2 = I s I b = ( E s ) 2 = I s The interference pattern looks the same. You can verify this yourself by taking a strand of your hair and a laser pointer. Shine the laser pointer at a wall and then put a strand of your hair in front of the light beam. The resulting interference pattern is the exact same as one would obtain from a slit with the same width as your hair.

We can use Babinet's Principle to solve complex problems. For example, say you have square aperture with sides of length L L . The the diffraction pattern for light passing through it is E = ɛ A e i ( k r ω t ) L 2 R [ sin β L β L ] [ sin α L α L ] E = ɛ A e i ( k r ω t ) L 2 R [ sin β L β L ] [ sin α L α L ] where (assuming the aperture lies in the y z y z plane) β L = k L Y / 2 R β L = k L Y / 2 R α = k L Z / 2 R . α = k L Z / 2 R . Now put an opaque square of length d d in the middle of the aperture. Now the resulting E E field is E = ɛ A R e i ( k r ω t ) [ L 2 sin β L β L sin α L α L d 2 sin β d β d sin α d α d ] E = ɛ A R e i ( k r ω t ) [ L 2 sin β L β L sin α L α L d 2 sin β d β d sin α d α d ] or I = I 0 [ L 2 sin β L β L sin α L α L d 2 sin β d β d sin α d α d ] 2 I = I 0 [ L 2 sin β L β L sin α L α L d 2 sin β d β d sin α d α d ] 2 β L = k L Y / 2 R β L = k L Y / 2 R α L = k L Z / 2 R . α L = k L Z / 2 R . β d = k d Y / 2 R β d = k d Y / 2 R α d = k d Z / 2 R . α d = k d Z / 2 R .

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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