erect.

As the object is withdrawn the image increases in size, still remaining erect, until we reach the principal focus, when we are unable to perceive any image. As the object is still withdrawn, a magnified but inverted image may be seen by placing the eye considerably farther away than the object.

When the object is at the centre the image is there also.

Lastly, if the object be beyond the centre, we have an inverted image nearer than the object, and less than it; and if the object be still withdrawn, this inverted image becomes smaller and smaller, until it finally vanishes from the sight.

267. Parabolic Mirrors. In a spherical mirror the image of a point of light, such as a star, is only brought approximately to a focus: but the case is different if we employ a parabolic mirror, that is to say, a mirror whose surface is that formed by the revolution of a parabola about its axis. In this case, if a luminous point, such as a star, be placed at an infinite distance along the axis, the rays which strike the mirror will do so in lines parallel to the axis, as in Fig. 77.

Let CD be one of these lines striking the surface at the point D, let E F denote a tangent to the parabola, and let Dƒ be the line joining D and the focus of the parabola.

Now it is a well-known property of the parabola that in all such cases the angle C D F is equal to the angle E Dƒ, and hence if CD be a line of light incident on the surface of the parabola at D, which surface we may there suppose to coincide with its tangent plane, it will be reflected in the direction Df, so that the reflected ray will pass through the focus of the

parabola. In like manner, the reflexion of any other ray of light coming from the star will pass through the geometrical focus of the mirror. Therefore in the case of a parabolic mirror and a star placed along its axis, the geometrical focus is not only approximately, but strictly, the optical focus.

On the other hand, if a luminous point were placed in the focus of a parabolic mirror, its rays would be reflected in lines strictly parallel to the axis.

Parabolic mirrors present, therefore, certain advantages over circular mirrors; but, on the other hand, it is difficult to construct them accurately.

268. Convex Mirrors.-We have dwelt on concave mirrors because they are the most important. We shall only state that in convex spherical mirrors the foci are all virtual, the reflected rays appearing to proceed from a point behind the mirror.

LESSON XXIX.-REFRACTION OF LIGHT.

269. Allusion has already been made (Art. 253) to the bending of a ray as it passes from one medium to another. This bending is called the refraction of light.

bent towards the perpendicular, as we see in the figure. There are two laws which regulate the path of the refracted ray. In the first place, CD, DE are in the same plane with

R

erect. As the object is withdrawn the image increases in size, still remaining erect, until we reach the principal focus, when we are unable to perceive any image. As the object is still withdrawn, a magnified but inverted image may be seen by placing the eye considerably farther away than the object.

When the object is at the centre the image is there also.

Lastly, if the object be beyond the centre, we have an inverted image nearer than the object, and less than it ; and if the object be still withdrawn, this inverted image becomes smaller and smaller, until it finally vanishes from the sight.

267. Parabolic Mirrors. In a spherical mirror the image of a point of light, such as a star, is only brought approximately to a focus: but the case is different if we employ a parabolic mirror, that is to say, a mirror whose surface is that formed by the revolution of a parabola about its axis. In this case, if a luminous point, such as a star, be placed at an infinite distance along the axis, the rays which strike the mirror will do so in lines parallel to the axis, as in Fig. 77.

Let CD be one of these lines striking the surface at the point D, let E F denote a tangent to the parabola, and let Df be the line joining D and the focus of the parabola.

Now it is a well-known property of the parabola that in all such cases the angle C D F is equal to the angle E Dƒ, and hence if CD be a line of light incident on the surface of the parabola at D, which surface we may there suppose to coincide with its tangent plane, it will be reflected in the direction Dƒ, so that the reflected ray will pass through the focus of the

parabola. In like manner, the reflexion of any other ray of light coming from the star will pass through the geometrical focus of the mirror. Therefore in the case of a parabolic mirror and a star placed along its axis, the geometrical focus is not only approximately, but strictly, the optical focus.

On the other hand, if a luminous point were placed in the focus of a parabolic mirror, its rays would be reflected in lines strictly parallel to the axis.

Parabolic mirrors present, therefore, certain advantage's over circular mirrors; but, on the other hand, it is difficult to construct them accurately.

268. Convex Mirrors.-We have dwelt on concave mirrors because they are the most important. We shall only state that in convex spherical mirrors the foci are all virtual, the reflected rays appearing to proceed from a point behind the mirror.

LESSON XXIX.-REFRACTION OF LIGHT.

269. Allusion has already been made (Art. 253) to the bending of a ray as it passes from one medium to another. This bending is called the refraction of light.

bent towards the perpendicular, as we see in the figure. There are two laws which regulate the path of the refracted ray. In the first place, CD, DE are in the same plane with

R

F DG, the normal to the plane at D; and in the next place, for the same medium, whater er be the incidence, the sine of the angle CDF or angle of incidence, always bears a fixed proportion of that of GDE or angle of refraction.

270. This may be expressed as follows: take equal lengths, C D D E, of the incident and refracted rays, and drop CF and EG perpendicularly upon the normal, then for the same substance the ratio between CF and GE will always be the same, whatever be the direction of the incident ray.

E

FIG. 79.

Again, if the ray of light, instead of passing from vacuo into the medium, passes out from the medium into vacuo, we have only to suppose the direction reversed; that is to say, if ED be a ray in the substance passing out at D, it will be bent from, not towards the perpendicular into the direction DC. Another noteworthy point is, that when a ray strikes the surface of a medium at right angles it suffers no refraction, for in this case the sine of the angle of incidence, or C D F,