Foci of Concave Mirrors
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-450
2025-12-17
24
Foci of Concave Mirrors. -There are six cases that can be considered.
- When the Source of Light is at an Infinite Distance. - In this case the rays of light will be parallel to the principal axis. The direction of the reflected ray MF (Fig. 1) is determined by drawing the normal from M to the center of curvature C, and making the angle of reflection CMF equal to the angle of incidence CMD. This reflected ray will cut the principal axis in F, a point practically halfway between C and A. By a similar construction it can be shown that other parallel rays will pass through F; hence F is at the principal focus.
- When the Source of Light is at a Finite Distance beyond the Center of Curvature. - In this case the rays of light will diverge, as from the point P (Fig. 2). The direction of any ray, as PM, after reflection is found by making the angle CMP' equal to the angle CMP. Other rays from P striking the mirror will, after reflection, meet at P', which is a point between the center of curvature and the principal focus.
- When the Source of Light is at the Center of Curvature. - Since every line from the center of curvature to the mirror is a radius of the mirror, it is evident that the focus will be found at C .
- When the Source of Light is between the Center of Curvature and the Principal Focus. - This is the converse of case (b), and by reference to Fig. 2it will be seen that the focus of P' is P, a point beyond the center of curvature.
- When the Source of Light is at the Principal Focus. -This is the converse of case (a). When the source of. light is at F (Fig. 1), the direction of every ray after reflection will be parallel to the principal axis; that is, the focus will be at an infinite distance - in other words, there M will be no focus.
- When the Source of Light is between the Principal Focus and the Mirror. - By making the angle of reflection equal to the angle of incidence CMP (Fig. 3), it will be seen that the reflected rays diverge from the principal axis as though they came from a point P' behind the mirror. This point P' is a virtual focus.
Demonstration. - By allowing parallel rays of light to fall upon the screen of the optical disk, the location of the principal focus of a concave mirror can be readily seen. The principal focal length is practically half the radius of the mirror.
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