Figure 2-33. Deviation of rays by two prisms, apex to apex

TM 9-258

b. Divergent Lens. A lens of a different type can be

2-16. Total Internal Reflection and Critical Angle.

approximated by placing two prisms apex to apex (fig 2-

33). If rays of light strike the front surfaces of the prisms,

a. When light passing from air into a more optically

the rays will pass through and, in accordance with the

dense medium, such as glass, strikes the boundary

law of refraction, those passing through the upper prism

surface, it is refracted. This occurs regardless of the

will travel upward while those passing through the lower

incident angle except when light is on the normal (no

prism will travel downward. Now assume that the front

refraction occurs). However, when light attempting to

and rear surfaces of this pair of prisms have been

leave a more optically dense medium for a less optically

rendered spherical and that the two prisms have been

dense medium strikes the boundary surface, it may be

converted into a lens (fig 2-34). All rays of light, except

reflected rather than refracted even though both

the axial ray, passing through this lens would spread out

mediums are perfectly transparent. This is known as

or diverge but instead of splitting in two at the axis would

total internal reflection and occurs when the incident

diverge evenly in a spherical manner. This type of lens

angle exceeds a certain critical angle. The critical angle

is known as a divergent lens. (All divergent lenses are

depends upon the relative indices of refraction of the

thicker at the edges than at the center.

media. Critical angles for various substances, when the

external medium is air, are listed in paragraph 2-17.

b. The total internal reflection of light can be

illustrated by following the rays from a light source under

water. Water has a critical angle of 480 36 minutes,

when the external medium is air. Rays of light from such

a source would be incident at various angles on the

surface separating the water and air (fig 2-35). As the

angle of incidence of the light rays increases, the

deviation of the refracted rays becomes proportionately

greater. A point is reached where an incident ray is

deviated to such an extent that it travels along the

surface of the water and does not emerge into the air.

The angle formed by this incident ray and the normal is

the critical angle of the medium.

Figure 2-33. Deviation of rays by two prisms, apex to

apex.

Figure 2-34. Deviation of rays by divergent lens.

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