332 



SCIENTIFIC AMUSEMENTS. 



CHAPTER XXIII. 



REFLECTION AND REFRACTION AT CURVED SURFACES. 



Expt. 361. Geometrical Focus of a Concave Mirror. When 

 a beam of light emanating from an object at a considerable distance 

 (e.g., the sun) falls upon a reflecting surface which is not flat (or 

 plane), but curved regularly (e.g., when the surface is part of a 

 sphere), the rays which fall upon different parts of the surface 

 will necessarily be reflected in different directions, even though 

 originally parallel to one another. In such a case the law of 

 reflection applies uniformly to every part of the surface, the normal 

 at the point of incidence (Expt. 332) being in each case the line 

 drawn perpendicular to the plane which is tangential to the surface 

 at the point where the incident ray falls *. 



Fig. 177 accordingly indicates the way in which two rays, SA, SB, 



would be reflected if 

 incident upon opposite 

 sides of the centre of 

 a concave mirror when 

 placed directly oppo- 

 site to the sun. If C 

 be the centre of the 

 spherical surface, the 

 normal at any given 

 point on the surface 

 will be a continuation 

 of the radius passing 

 through that point. 

 Hence, for the points A 

 and B the respective 



Fig. 177. Real Focus of Concave Mirror. 



normals are the lines CAD, CBE. Hence, the lines AF, BF, 

 representing the reflected rays (so situated that the angles SAC 

 and CAF are equal, and also the angles SBC and CBF are equal), 

 will converge so as to cross one another at a point F. The same 



* A plane tangential to a curved surface may be illustrated by a flat slate 

 touching a round cricket ball or orange ; the plane of the slate's surface 

 touches or is tangential to the curved surface of the ball at the point where 

 the two surfaces meet. A line drawn perpendicular to the surface of the 

 slate through this point would represent the normal at the point of incidence 

 in reference to a ray of light incident upon the curved surface at that point. 



