Section 20. Thin Prisms

Transcription

1 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp 0- Section 0 Thin Prisms

2 Thin Prism Deviation Thin prisms introuce small angular beam eviations an are useful as alignment evices. The beam eviation is approximately inepenent of the incient angle: n The beam eviation is parallel to a principal section of the prism an towars the thick en of the prism. n 0 z 0- OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp Thin prisms are use for optometric correction of strabismus (a misalignment of the axes of the eyes). The eviation is measure in prism iopters. A prism of iopter eviates a beam by cm at m. For small eviations: D ( in 0.0 raians)

3 Thin Prism Deviation - Derivation sin n sin sin cossin sin sin 3 Neglect terms in, an higher: sin n / n / n /n sin n / n 3 sin x xx / 6... sin n / n n / n 3 n / 6 n 0-3 z OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp n / n n / n n n n n n For small: n

4 Thin Prism Deviation Alternate Derivations The thin prism is always use at minimum eviation. Tip the prism so that the front face is perpenicular to the input ray: Snell's Law: n n n At minimum eviation: n z 0-4 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp n sin MIN / sin / n n

5 ombinations of Thin Prisms The beam eviation is parallel to a principal section of the prism an towars the thick en of the prism. The magnitue an irection of this eviation efines a vector perpenicular to the optical axis (in the x-y plane). Y y X x cos X sin Y 0-5 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp The net eviation vector for a series of thin prisms is the sum of the component vectors. y x

6 Two Thin Prisms Net eviation an irection: / cos( ) Y sin sin tan cos cos X Aing: y The net eviation is the sum of the iniviual eviations. x 0-6 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp Opposing: 80 The net eviation is the ifference of the iniviual eviations.

7 Risley Prism A Risley prism consists of a pair of ientical, but opposing, thin prisms. The prisms are counter-rotate by +/- to obtain a variable net eviation in a fixe irection (shown with the net eviation in the y-irection). y x 0 sin OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp The Risley prism allows the fine angular alignment of an optical system by ajusting the prism orientations.

8 Thin Prism Dispersion The ispersion of a thin prism measures the total angular sprea for to F light, an the seconary ispersion gives the sprea from the to wavelengths. The results epen on the inex n, Abbe number an partial ispersion ratio P of the glass. Deviation: Dispersion: Seconary Dispersion: ( ) n ( n )( ) ( n )( ) ( n n ) F F ( n )( ) ( n )( ) ( n n ) F 0-8 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp n n n F Abbe Number n n n n F P Partial Dispersion Ratio P

9 Thin Prism Dispersion an the hromatic Aberration of a Thin Lens The ege of a thin lens can be consiere to be a thin prism. The prism angle will epen on the power an iameter of the lens. Each wavelength will be eviate by a ifferent angle. The focal length of the lens is efine for light. r ( ) f = f F f Abbe Number: z n n F 0-9 n OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp ( ) ( n ) r f ( ) ( ) f r r r F F f f ff r r F F f r F f f f F F F r f f ( nf ) ( n ) nf n nf n f ( n ) ( n ) n F f f

10 Systems of Thin Prisms Deviations an ispersions a. An inverte prism (with its vertex at the bottom) eviates a ray up an has a negative vertex angle. Deviation: Dispersion: Seconary Dispersion: i i i i i i 0-0 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp

11 Achromatic Thin Prism An achromatic thin prism or achromatic wege provies eviation without ispersion. Opposing prisms mae from two ifferent glasses ( n,, P an n,, P ) are combine to force the ispersion between the F an wavelengths to be zero. 0 A eviation of is maintaine for light: ( ) ( ) n n n n OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp The high ispersion prism is inverte to obtain an opposing eviation.

12 Achromatic Thin Prism Seconary Dispersion The achromatic thin prism esign forces F an wavelengths to have the same eviation, but it oes not require that the wavelength have this same eviation. The resiual ispersion is the seconary ispersion. P P P From the achromatic conition: P ( ) F- 0- OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp ( ) P P PP P While the F an wavelengths are correcte, a resiual seconary ispersion remains. For most glass pairs, light will be bent more than the F an wavelengths.

13 Seconary Dispersion For most glasses: P 0 The shape of this curve epens on the etails of the two ispersion curves. The maximum ispersion oes not occur for -light. Simple thin prism: F 0-3 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp The ispersion is about.5-3% of the eviation. Achromatic thin prism: P P The resiual or seconary ispersion is about 0.05% of the eviation. The ispersion is reuce by a factor of about 40 over the simple thin prism.

14 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp Achromatic Prism How Does It Work? Low ispersion prism: High ispersion prism: 0-4

15 Direct Vision Prism A irect vision prism uses opposing prisms to provie ispersion without eviation of the light. An object viewe through this prism is smeare by the local spectrum of the object. For a esire ispersion : 0 n F 0-5 OPTI-0/0 Geometrical an Instrumental Optics opyright 08 John E. Greivenkamp n In orer to get sufficient ispersion, it is often necessary to use more than two prisms.