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Refraction by a Spherical Surface

Refraction by a Spherical Surface

Parallel rays passing through such a surface separating media of different density, do not continue parallel, but are refracted, so that they meet at a point called the principal focus.
If parallel rays E, D, E, fall on A B, a spherical surface separating the media M and N of which x is the denser; ray D, which strikes the surface of A B at right angles, passes through without refraction, and is called the principal axis; ray K will strike the surface at an angle, and will therefore be refracted towards the perpendicular C J, meeting the ray D at F ; so also witln ray E, and all rays parallel in medium M. The point F where these rays meet is the principal focus, and the distance between the principal focus and the curved surface is spoken of as the principal focal distance.

Fig 9

Rays proceeding from F will be parallel in M after passilig through the refracting surface. Rays parallel in medium N will focus at F', which is called the anterior focus

Had the rays in medium M been more or less divergent, they would focus on the principal axis at a greater distance than the principal focus, say at H; and conversely rays coming from H would focus at G; these two points arc then conjugate foci.

When the divergent rays focus at a point on the axis twice the distance of the principal focus, then its conjugate will be at an equal distance on the other side of the curved surface.

Fig 10

If rays proceed from a point O, nearer the surface than its principal focus, they will still he divergent after passing through A B, though less so than before, and will never meet by continuing these rays backwards they will meet at L, so that the conjugate focus of O will be at L, on the same side as the focus ; and the conjugate focus will in this case be spoken of as negative.