dull, and at the point of change a coloured band extends across the surface from left to right. Adjust the distance of the cube

from the slit till that part of the coloured band where violet shades off into green coincides with the diamond scratch on the face of the cube.

Measure h, the height of the slit, and h, the height of the line on the cube, above the surface of the scale, and d the horizontal distance between the face of the cube and a perpendicular let fall on to the scale from the slit.

Then if i angle of emergence of the ray from the cube

=

(Fig. 71), tan i = (h2 — h2)/d.

If r = the angle of incidence of the internal ray at C, and N = the index of refraction of the cube with respect to air for the light used, i.e. that near the Fline, then

sin i = N sin r.

Since total reflection just begins at B, i.e., the angle of incidence at B is the critical angle,

n = N cos r,

where n the index of refraction with respect to air of the liquid at B.

or

Squaring and adding the last two equations we get

n2 + sin2 i = N2

n = √ Na-sini.

From which n may be calculated if N is known and i is found by measurement of h, ha, and d.

Determine by this method the value of N for the cube for the line F, taking the index n for water to be 1·337.

Having found N find n for ethyl alcohol.

Arrange your observations as follows:

SECTION XXXVIII.

MAGNIFYING POWERS OF INSTRUMENTS.

Apparatus required: Telescope, microscope, millimetre

scales.

When an object is viewed through an optical instrument, such as a telescope or microscope, the apparent size of the image is in general larger than that of the object as seen direct, and it is the purpose of this exercise to determine the amount of magnification.

TELESCOPE.

The magnifying power of a telescope is defined as the ratio of the apparent size of the image seen through the telescope to the apparent size of the object as seen direct, the eye being in the same condition during the two observations. If F is the focal length of the objective, ƒ that of the eyepiece, and D is the distance of the object from the objective, it may be shewn that the magnifying power

To determine the magnifying power, direct the telescope towards some surface on which is a regular well-marked pattern of some kind, such as a divided scale or the dividing lines in a brick wall, and when the pattern has been focussed, look at it through the telescope with one eye and with the other direct. Move the head a little to the right or left and notice whether the pattern seen through the telescope appears to move across the

pattern seen direct. If so the focussing of the telescope should be altered slightly till one pattern is not displaced with respect to the other when the head is moved There is then no "parallax." Count how many times some convenient length in the magnified pattern contains the same length of the pattern seen direct. This number is the magnifying power of the telescope as used.

Measure the distance of the telescope from the pattern, move the telescope to another position and again find the magnifying power, and repeat the observations at 5 positions varying from as close to the wall as possible to a distance of 40 or 50 metres away.

Measure the focal length F of the objective by taking out the eyepiece of the instrument and holding a sheet of paper at the eye end, so that an image of a distant object formed by the objective is in focus on the sheet, the distance F of the paper from the objective is the focal length of the objective as follows:

Record

Hence the focal length f1 of the eyepiece = 22/16·3 = 1.35 cms.

MICROSCOPE.

The magnifying power of a microscope is defined as the ratio of the apparent size of the image as seen through the instrument, to the apparent size of the object, when each is at

S. P.

12

the standard nearest distance of distinct vision from the eye, i.e. 25 cms.

If f is the focal length of the eyepiece, fo that of the objective, d the distance of the first focal plane of the eyepiece from the objective, and do the standard least distance of distinct vision, the magnifying power of the instrument

In most cases d is nearly equal to l the length of the instrument, and the magnifying power then

Place a millimetre scale* on the stage of the microscope, and focus it distinctly. Mount another scale graduated in millimetres vertically 24 cms. to the left or right of the eyehole of the instrument with its centre in the same horizontal plane as the eyebole.

Place on the eyehole of the instrument a small strip of plane unsilvered glass mounted so that its normal makes an angle of 45° with the axis of the microscope. Look down the microscope through the glass, keeping the eye one centimetre above the eyehole. Adjust the glass till an image of the central part of the vertical scale is seen covering the central part of the image of the scale on the stage of the microscope. If the image of the stage scale is now indistinct, focus the microscope again. See that there is no parallax between the vertical scale and the image of the stage scale, then read on the image of the vertical scale the number of divisions equivalent to one of the stage scale. This is the magnifying power of the instrument. Measure the length of the microscope from the objective to the eyehole. Draw out the tube of the instrument, so that the length is increased about 3 cms. Raise the vertical scale by the same amount and repeat the observations. Continue the process till the tube is as long as it can be made. Measure

*If the magnifying power of the instrument is large a scale divided into tenths and hundredths of a millimetre should be used on the stage.