CH. XII] SIZE OF SCREENS 467 



If the lantern cannot be at the back of the room, but must be 

 closer to the screen, then the projection objective must be of shorter 

 focus than 25 to 30 cm. (10-12 in.). 



To determine the proper objective to use to give the desired size 

 of image in any case one must proceed as follows : 



1 i ) The size of screen image is decided on by remembering that 

 it should be between one-fourth and one-fifth the distance to the 

 farthest seat in the room. 



(2) The distance from the screen to the lantern must be 

 measured. 



(3) Following the simple optical law founded on the geometry 

 of similar triangles that: "The size of object and image vary 

 directly as their distance from the center of the objective," one 

 can by simple proportion get the focus which the objective should 

 have for a given screen image. 



637. Examples. For example, suppose the distance from the 

 screen to the farthest seat is 20 meters (66 ft.), the width of the 

 screen should be not less than one-fourth this distance, i. e., five 

 meters (16.5 ft.). 



Now suppose that instead of the lantern being 20 meters from 

 the screen it is only n meters (36 ft.) from it, what should be the 

 focus of the projection objective to give a screen image 5 meters 

 (16.5 ft.) wide? 



The formula best adapted for this calculation is: 



f d 



where f is the distance of the object from the center of the objective 

 (focus of the objective). 



is the size of the object. 



d is the distance from the objective to the screen. 



1 is the size of the screen image. 



It is assumed in all the calculations for the magic lantern that 

 the width of the lantern-slide opening or picture is 7.5 cm. or 3 

 inches. 



