Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Waves and Optics » Babinet's Principle

Navigation

Table of Contents

Lenses

What is a lens?

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? tag icon

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

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship display tagshide tags

    This collection is included in aLens by: Digital Scholarship at Rice University

    Comments:

    "This book covers second year Physics at Rice University."

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

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 .

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

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? tag icon

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

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

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? tag icon

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

| External bookmarks