THE OPTICS OF PHOTOGRAPHIC LENSES 



21 



the axial image point, one cosine is present because the aperture is projected as an 

 eUipse in the outer parts of the field, and the fourth arises from the obliquity of the 

 light as it falls on the plate (Fig. 17). Table V shows the variation in light inten- 

 sity on the photographic plate for various angles off the optical axis. 



The Vignetting Effect. — In addition to the loss of light caused by the cos^ <f> law 

 (Table V), in many lenses the mounts cut off oblique pencils more than axial pencils, 

 causing the illumination in the outer parts of the picture to be still less (Fig. 18). 



v_y 



Diagram illustrating vignetting effect. 



To an eye at A, the lens has a circular aperture, but viewed from B, the aperture is 

 limited by the overlap of two ellipses, as shown at the right of Fig. 18. The com- 

 bination of the cos** 4) relation with vignetting may produce such a diminution of light 

 that the corners of thephotographic print appear dark, and sometimes almost black. 

 The vignetting effect can generally be reduced by stopping the lens down. 



The magnitude of the vignetting effect can readily be determined by the arrange- 

 ment shown in Fig. 19. In this diagram, S represents a lamp and G an opal-glass 



6 R P 



Fig. 19. — Diagram showing the measurement of vignetting effect. 



plate before the lens L to be investigated. R is a, row of pinholes in a metal screen 

 placed in the focal plane of the lens and near a photographic plate P. Each pinhole 

 in R will project on the plate a picture of the shape of the lens aperture correspond- 

 ing to the particular point in the field occupied by the pinhole. 



The Light Transmission of a Lens. — It might be thought that as a lens is made of 

 glass, its light transmission would be determined only by the transparency of the 

 glass itself. This is unfortunately very far from the case because a surface separating 

 air from a medium of refractive index n reflects back a proportion [{n — l)/{n + 1)]^ 



