The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful arts — John Shaqi
The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful artsBrewster, David
Science
The kaleidoscope : $b its history, theory and construction. With its application to the fine and useful arts
Brewster, David
Kaleidoscopes
+---------------+---------------+
| Complement of | Rays Reflected|
| the Angles | out |
| of Incidence. | of 1000. |
+---------------+---------------+
| 2½° | 584 |
| 5 | 543 |
| 7 | 474 |
| 10 | 412 |
| 12½ | 356 |
| 15 | 299 |
| 20 | 222 |
| 21 | 210 |
| 25 | 157 |
| 26 | 149 |
| 30 | 112 |
| 31 | 105 |
| 34 | 85 |
| 35 | 79 |
| 36 | 74 |
| 37 | 69 |
| 38 | 65 |
| 39 | 61 |
| 40 | 57 |
| 46 | 40 |
| 50 | 34 |
| 55 | 29 |
| 60 | 27 |
| 70 | 25 |
| 80 | 25 |
| 90 | 25 |
+---------------+---------------+
In order to explain the method of using the table, let us suppose that
the angle of incidence, or =O R _p_=, Fig. 19, is 85°: then the number
of rays in the corresponding point π of the reflected sector =A O _b_=
(Fig. 17) will be 543. By letting fall perpendiculars from the points
μ, π, upon the mirror =B O=, and taking =O _p_=, =O _n_=, Fig. 19,
equal to these perpendiculars, we may ascertain the angles at which the
light from the points μ, π, suffer a second reflexion from the mirror
=B O=. Let the angle for the point π be 10°, then the number of rays
out of 1000 reflected at this angle, according to the table, is 412;
but as the number of rays emanating from π, and incident upon =B O=, is
not 1000, but only 543, we must say as 1000: 412 = 543: 224, the number
of rays reflected from =B O=, or the intensity of the light in a point
in the line =O _bʹ_= corresponding to π.
[Illustration: FIG. 19.]
The preceding method of calculation is applicable only with strictness
to the two sectors =A O _b_=, =B O _a_=, formed by one reflexion, for
the intensity of the light in the other sectors which are formed by
more than one reflexion, must be affected by the polarization which
the light experiences after successive reflexions; for light which has
acquired this property is reflected according to laws different from
those which regulate the reflexion of direct light.
When the mirrors are metallic, the quantity of reflected light is also
affected by its polarization, but it is regulated by more complicated
laws.
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