416 SHADOW. 



the opaque body which causes the shadow, whatever. the 

 distance between the opaque body and the screen on 

 which the shadow is received. If the opaque body is 

 larger than the source of light, as is the case with K^ 

 the umbra (defined by the lines a c and b d) will increase 

 in length and width as the distance between screen and 

 body increases. Finally, if the opaque body is smaller 

 than the source of light, as K^ the umbra (between a g 

 and b g) decreases as the distance of the screen from the 

 body increases, and 110 umbra is produced when the screen 

 is removed beyond a certain point, here indicated by g. 

 An eye which is situated within the true shadow of 

 a body cannot see anything of the source of light ; the 

 latter is completely covered by the body which causes 

 the shadow. 



A certain portion of space round the umbra is par- 

 tially obscured ; this space receives light only from a 

 portion of the luminous body, and is called the 'partial 

 shadow ' or penumbra. The limits of the penumbra are 

 found by drawing straight lines from the highest point of 

 the source of light past the lowest point of the opaque 

 body, and from the lowest point of the former past the 

 highest point of the latter (a i, b A, a I, bk, an, b m) 

 or, generally, lines must be drawn from one side of the 

 circumference of the luminous body to the opposite side 

 of the circumference of the opaque body. 



The penumbra is not equally dark throughout, like 

 the umbra ; where it adjoins the umbra it is so dark that 

 it can hardly be distinguished from the latter, but it be- 

 comes gradually less and less dark towards the external 

 boundary and there it passes imperceptibly into the 

 space upon which the light falls freely. In all cases, as 



