Review on Lenses
Thin lenses
Approximations (We got to ensure these conditions are
fulfilled in the lab)
Only spherical surfaces (constant curvature).
Paraxial approximation: rays are near the optical axis and
almost parallel to it.
Deviations from this approximations are called aberrations.
For our purposes:
Lenses are characterized by their focal length f which in turns
depends on the material it is made and its geometry.
1
= (n − 1)
f
1
1
−
R1
R2
.
n = refraction index
.
R1 and R2 = curvature radii of lens’ surfaces.
Review on Lenses
Type of lenses
Biconvex
Plano-convex
Positive
meniscus
Negative
meniscus
Plano-concave
Biconcave
R1 > 0
R2 < 0
R1 > 0
R2 = ∞
R1 > 0
R2 > 0
R1 > 0
R2 > 0
R1 = ∞
R2 > 0
R1 < 0
R2 > 0
If they are thin enough they obey:
1
1
1
+
=
so
si
f
Here so and si are the distances from the centre of the lens to the
object and to the image respectively.
Review on Lenses
Sign conventions
We follow these conventions to facilitate the calculations of formation
of images
Notation:
.
f = focal distance
.
so = object distance
.
si = image distance
1
Initially light goes from left to right (object or source of light is
on the right side).
2
f > 0 (f < 0) for converging (diverging) elements.
3
so > 0 (so < 0) if the object is on the left (right) of the lens.
4
si > 0 (si < 0) if the image is on the right (left) of the lens.
Review on Lenses
Combination of lenses
Any combination of any number of lenses
can be thought to be an effective lens with an effective focal distance.
1
1
d
1
=
+
−
f
f1
f2
f1 f2
For N lenses attached together:
1
1
1
1
1
=
+
+
+ ··· +
f
f1
f2
f2
fN
Assuming all the lenses are extremely thin, so that the effective lens is
thin as well.
Review on Lenses
Magnification of a lens
Finally the image size relates to the location of the object and the
image.
Transverse Magnification
M=
hi
si
=−
ho
so
The minus sign indicates if the image is above or below the optical
axis.
Longitudinal Magnification
M` = M 2