1. Equations for thin lens calculations. The thin lens equation is given by Equation 3-10.


where p is the object distance (from object to lens vertex V)

q is the image distance (from image to lens vertex V)

and f is the focal length (from either focal point F or F′ to the lens vertex V)

For a lens of refractive index ng situated in a medium of refractive index n, the relationship between the parameters n, ng, r1, r2 and the focal length f is given by the lensmaker’s equation in Equation 3-11.


where n is the index of refraction of the surrounding medium
ng is the index of refraction of the lens materials
r1 is the radius of curvature of the front face of the lens
r2 is the radius of curvature of the rear face of the lens

The magnification m produced by a thin lens is given in Equation 3-12.


where m is the magnification (ratio of image size to object size)
hi is the transverse size of the image
ho is the transverse size of the object
p and q are object and image distance respectively

2. Sign convention for thin lens formulas. Just as for mirrors, we must agree on a sign convention to be used in the application of Equations 3-10, 3-11, and 3-12. It is:

• Light travels initially from left to right toward the lens.