» Lummer–Gehrcke plate (0556)
Immagini
DESCRIPTION
Exhibit 556 is the Lummer-Gehrcke inferential laminar structure for studying the interference of light waves. On a spectroscope light from an arbitrary source is passed through a slit and collimated so that the beam incident on the total internally reflecting prism is parallel. This beam is then directed onto the parallel quartz plate where the angle of incidence is slightly less than the critical angle so that successive reflections and refractions lead to two sets (one above and one below the quartz plate) each of several (weak) refractive rays that serve as virtual sources which interfere constructively and destructively in an image formed by a collecting lens (See design-1). These rays are then observed with a telescope.
It is used with the interferential spectroscope (exhibit 401) to observe interference in luminous waves.
A light ray (AB) is incident on the surface (XY)of the quartz plate at an angle(i); a part reflects along (BC) and a part refracts along (BD). At point (D) this part reflects along (DE) and a part refracts along (DK). The same at point (E). In this way one obtains two rays reflected (BC) and (EF). Vedi Disegno-2.
If μ is the index of refraction of the quartz plate, the difference in the optical path 'd' between (BC) and (BF) is![Equazione: [d =\mu({\bf BD} +{\bf DE}) - {BP} \eqno{1}]](/foto/equaz/556_eq01.png "Equazione: [d =\mu({\bf BD} +{\bf DE}) - {BP} \eqno{1}]")
![Equazione: [{\bf BD} = {\bf DE} = \frac{t}{\cos r}]](/foto/equaz/556_eq02.png "Equazione: [{\bf BD} = {\bf DE} = \frac{t}{\cos r}]")
![Equazione: [{\bf BQ} = {\bf QE} = t (\tan r)]](/foto/equaz/556_eq03.png "Equazione: [{\bf BQ} = {\bf QE} = t (\tan r)]")
Therefore:
![Equazione: [\mu ({\bf BD} +{\bf DE}) = \frac{2\mu t}{\cos r}\eqno{2}]](/foto/equaz/556_eq04.png "Equazione: [\mu ({\bf BD} +{\bf DE}) = \frac{2\mu t}{\cos r}\eqno{2}]")
![Equazione: [{\bf BP} = 2{\bf QE}\sin i = 2t\mu\frac{sin^2r}{\cos r}\eqno{3}]](/foto/equaz/556_eq05.png "Equazione: [{\bf BP} = 2{\bf QE}\sin i = 2t\mu\frac{sin^2r}{\cos r}\eqno{3}]")
being:
![Equazione: [ \sin i= \mu\sin r ]](/foto/equaz/556_eq06.png "Equazione: [ \sin i= \mu\sin r ]")
Substituting (2) e (3) in (1) one obtains the optical path difference
![Equazione: [ d= 2\mu t\cos r ]](/foto/equaz/556_eq07.png "Equazione: [ d= 2\mu t\cos r ]")
Where r is the refraction angle and t is the thickness of the plate;.
For a constructive interference (that is, a luminous fringe) the optical path difference is
![Equazione: [ d = 2\mu t\cos r=n\lambda ]](/foto/equaz/556_eq08.png "Equazione: [ d = 2\mu t\cos r=n\lambda ]")
The set of maxima that are formed for different λ and for a fixed value of 'n' has the name spectra of order n where
![Equazione: [ n = \frac{2\mu t\cos r}{\lambda} ]](/foto/equaz/556_eq09.png "Equazione: [ n = \frac{2\mu t\cos r}{\lambda} ]")
.
BIBLIOGRAPHY
- [1] Perucca E.,"Fisica Generale e Sperimentale" Vo. II, UTET Torino, 1937. § 111, Page188.
- [2] Worsnop B.L. and Flint H.T., "Advanced Practical Physics For Students", Asian Edition, 1961. (Page 372 -- 377)
Dati Catalografici
| Data di costruzione: | ca 1920 |
|---|---|
| Data di carico: | 1923-06-28 |
| Nr. Inventario: | 4062 (Generale dal 1874) |
| Costruttore: | Costruttore sconosciuto |
| Materiale: | vetro |
| Dimensioni: | 13 cm x 0,8 cm x 0,8 cm |
| Conservazione: | buono (Sono disponibili due Lamine nei loro astucci: un astuccio inventariato 4062 contiene una "Lamina di Lummer e Gehrcke" rotta in tre pezzi mentre l'altro non ha numero di inventario e contiene una lamina in perfette condizioni, identica alla prima. E' possibile che una lamina si sia rotta durante il trasporto (forse dalla Germania), e sia stata sostituita con una nuova, senza più procedere all'inventario.) |