Thin Lenses
Thin lens approximation –
The thickness of the lens is assumed to be negligible
This allows us to assume that the distance from the surface of the lens
to the focal point is the same as the distance from the center of the lens
to the focal point (i.e., focal length remains uniform throughout thickness of
lens)
Lens Makers’ Equation
Focal length for a lens in air is related to the curvature of its front and back
surfaces (R1 and R2) and to the index of refraction, n, of the lens material.
Sign convention of lens radii R1 and R2 The signs of the lens radii indicate
whether the corresponding surfaces are convex (R > 0, bulging outwards from
the lens) or concave (R < 0, depressed into the lens). If R is infinite, the surface
is flat, or has zero curvature, and is said to be planar.
Power of a lens
P (diopters) = 1/f( meters)
Sign Convention for Thin Lenses
The sign conventions for the given quantities in the mirror equation and
magnification equations are as follows:
fis + for a converging lens
fis - for a diverging lens
do is + if the object in front of lens dois - if the object is in back of lens
diis + if the image is in back of lensdiis - if the image is front of lens
R1and R2are + if the center of curvature for each surface is in back of the lens
R1and R2are - if the center of curvature for each surface is in front of the lens
Example 25.42
A thin double concave lens (diverging) has a refraction index of n = 1.5. The radius
of the first surface is 15 cm and the radius of the second surface is 10 cm. Find the
focal point, f, of the lens. Determine the position for object distances of infinity, 3f,
f, and f/2.
Multiple Lenses
If two lenses are used to form an image, the image of the first lens is treated
as the object of the second lens.
The overall magnification for the system, is the product of the magnifications
for the individual lens.
Example 25.53
Two converging lenses, each of focal length 15 cm, are placed 40 cm apart, and
an object is placed 30 cm in front of the first. Where is the final image formed,
and what is the magnification of the system?
Example 25.60
A lens and mirror system have focal lengths of +80 cm and -50 cm,
respectively. An object is placed 1.0m to the left of the lens. Locate the final
image and determine the magnification and whether it is upright or inverted.