The Lines of Fraunhofer

1814 · Spectroscopy · The companion to Plate IV

How many slits a grating needs to show sodium’s D line as two, worked out step by step.

A Demonstration is a plate’s companion print: the reasoning behind the discovery, worked out on a sheet of its own.

Paper ground, a warm cream, on Hahnemühle Photo Rag, 308 gsm cotton

The plate it accompanies

Plate IV, The Lines of Fraunhofer: Dark lines in sunlight tell us what the Sun is made of. See it

What it shows

Plate IV shows sunlight spread into its colours and crossed by dark lines. Joseph von Fraunhofer mapped the lines in 1814, and in 1821 he measured their wavelengths with gratings he made by stretching fine wires across a frame. This sheet starts from his grating No. 1. From the spacing of its wires and the angle through which it bent the light of the D line, it works out the wavelength of D as Fraunhofer did, and finds 589.0 nanometres.

Fraunhofer also saw that D is two lines close together, which modern measurements put at 588.995 and 589.592 nanometres. Each bright line a grating makes grows narrower as slits are added, and the sheet works out how narrow the lines must be before the pair can be seen as two. By Rayleigh’s rule, a grating needs at least 987 slits to show sodium’s D as two lines in the first order.

Fraunhofer’s 1821 values for three of his lines sit on the sheet beside today’s. He gave them, as he gave the widths of his wires, in fractions of a Paris inch. Converted, each comes within a nanometre of today’s value.

Close up, at about the size it prints at Medium

Step 6 of the sheet: the solar spectrum around sodium’s D line, two deep dips with a yellow band between them. — Step 6. Sunlight near the D line, from the Kitt Peak atlas that the plate’s strips are drawn from. The yellow band spans the 0.597 nanometres between the two dark lines.

Step 7: two bright peaks drawn dotted and their sum drawn solid, with a blue bracket spanning the yellow band between the peaks. — Step 7. Through a grating of 987 slits, one line’s peak stands on the other’s first dark. The two lines then show as two peaks with a dip between them.

A table of Fraunhofer’s 1821 values for the C, D and E lines beside today’s wavelengths. — Fraunhofer’s values from 1821 beside today’s, for three of his lines. He gives D as 0.00002176 of a Paris inch, which is 589.0 nanometres.

Hang them together

Plate IV

Demonstration IV

Demonstration IV is the companion to Plate IV, The Lines of Fraunhofer, which shows the dark lines in sunlight. Hung side by side in the same size and frame, the two cost 10% less bought together.

Plate IV and Demonstration IV, Medium, 42 × 59 cm each, in black frames.

The sheet

Fraunhofer’s grating measurements of 1821, with Rayleigh’s rule for telling two lines apart and modern measurements of sodium’s D

1Fraunhofer’s grating No. 1
2The path difference between neighbouring slits
3The wavelength of D, from his measurement
4Slits that cancel in pairs
5How narrow a bright line is
6The two lines of D in sunlight
7The slits needed to show D as two lines
†And a question to take further: how much light is left halfway between the two peaks

Sizes and prices

Size	Unframed	Framed	Print
Medium42 × 59 cm	£95$145	£225$295	420 × 594 mm
Large59 × 84 cm	£160$215	£390$515	594 × 841 mm
Extra large84 × 119 cm	£285$385	Unframed only	841 × 1189 mm

Paper: Hahnemühle Photo Rag, 308 gsm cotton, printed as a giclée by theprintspace.
Printed in: London for the UK, Brooklyn for the US. Unframed prints travel rolled in a tube.
Framed medium: A2 frame, glazed with 3 mm acrylic.
Framed large: A1 frame, glazed with 3 mm acrylic.
Extra large: unframed only. A0 is a standard frame size.
Frames: solid wood, finished in black, white or oak veneer, made in Germany. Each comes ready to hang.
Edition: open, with a certificate. File version v1.