The Spectro-Photometer

This instrument consists of a long, flat rectangular box (fig. 41). At one end of this there is a slit, A, the width of which can be adjusted. The white light from a source behind the slit passes through a collimating lens, L, placed at the distance of its own focal length from A, and falls as a parallel pencil on the set of direct-vision prisms SS'. The emergent beam is brought to a focus by the second lens M, and a pure spectrum thus formed at the end of the box.

A sliding-piece fitted to this end carries a narrow slit B, through which any desired part of the spectrum may be viewed, C is a second slit, illuminated also by white light, the rays from which after passing through the lens N fall on a plane mirror K, and being there reflected traverse the prisms and form a second spectrum directly below the first. By adjusting the positions of the lenses and the mirror K the lines in the two spectra can be made to coincide. The light from A passes over the top of the mirror and the two spectra are seen one above the other. A concave lens enables the observer to focus distinctly the line of separation.

In front of the three slits respectively are three Nicol's prisms, F, G, H. F is fixed with its principal plane vertical, parallel, therefore, to the slits and edges of the prisms; G has its principal plane horizontal, while H is capable of rotation round a horizontal axis parallel to the length of the box; P is a pointer fixed to the prism H and moving over a graduated circle Q R, which is divided into 360 parts. The zero of the graduations is at the top of the circle, and when the pointer reads zero the principal plane of H is vertical.

The Nicols F and G polarise the light coming through the slits, the first in the horizontal plane, the second in the vertical The emergent beam is analysed by the Nicol H. When the pointer reads zero or 180° all the light in the upper spectrum from the slit A passes through H, but none of that from C is transmitted. As the Nicol is rotated through 90° the quantity of light from A which is transmitted decreases, while the amount coming from C increases, and when the Nicol has been turned through 90° all the light from c is transmitted and none from A.

For some position then between 0 and 90° the brightness of the small portions of the two spectra viewed will be the same. Let the reading of the pointer when this is the case be θ. Let the amplitude of the disturbance from A be a, that of the disturbance from C be c, then clearly

and if I_a, I_c be the respective luminous intensities,

Now place anywhere between L and K a small rectangular cell containing an absorbing solution. The upper spectrum will become darker and the Nicol will require to be moved to establish equality again in the brightness. Let θ' be the new reading, and I_a' the intensity of the light which now reaches the eye from A. Then₍₁₎

Thus

But if k represent the fraction of the light lost by absorption and reflexion at the faces of the vessel, we have

Hence

To eliminate the effects of the vessel the experiment should be repeated with the vessel filled with water or some other fluid for which the absorption is small; the difference between the two results will give the absorption due to the thickness used of the absorbing medium.

Of course in all cases four positions of the Nicol can be found in which the two spectra will appear to have the same intensity. At least two of these positions - which are not at opposite ends of the same diameter - should be observed and the mean taken. In this manner the index error of the pointer or circle will be eliminated.

For success in the experiments it is necessary that the sources of light should be steady throughout. In the experiments recorded below two argand gas-burners with ground-glass globes were used. The apparatus and burners must remain fixed, relatively to each other, during the observations.(2)

Mr. Lea has recently suggested another method of using the instrument to compare the concentration of solutions of the same substance of different strengths.

A cell is employed with parallel faces, the distance between which can be varied at pleasure. A standard solution of known strength is taken and placed in a cell of known thickness; let c₁ be the concentration, that is, the quantity of absorbing matter in a unit of volume, m₁ the thickness of this solution. The apparatus is adjusted until the intensity in the two images examined is the same. The other solution of the same medium is put in the adjustable cell, which is then placed in the instrument, the standard being removed, and the thickness is adjusted, without altering the Nicols, until the two images are again of the same intensity, whence, if c be the concentration, m the thickness, we can show that

and from this c can be found, for all the other quantities are known.

We may arrive at equation (1) from the following simple considerations. If c be the concentration, cm will be proportional to the quantity of absorbing material through which the light passes. If, then, we suppose that with the same absorbent the loss of light depends only on the quantity of absorbing matter through which the light passes, since in the two cases the loss of light is the same, we must have

or

Experiments.

(1) Determine by observations in the red, green, and blue parts of the spectrum the proportion of light lost by passing through the given solution.

(2) Determine by observations in the red, green, and blue the ratio of the concentration of the two solutions.

Enter results thus:

(1) Solution of sulphate of copper i cm. in thickness.

(2) Two solutions of sulphate of copper examined. Standard solution, 10 percent, 1 cm. in thickness. Thickness of experimental solution giving the same absorption observed, each mean of five observations.

Color of Light	Thickness	Ratio of Concentrations
Blue	74	1.35
Green	73	1.37
Red	75	1.33

(1)	See Glazebrook, Physical Optics, pp. 10-27
(2)	See Proc. Cam. Phil. Soc., vol. iv. Part VI. (Glazebrook on a Spectro-photometer)