Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Topics
 Measuring:
• Radii of mirrors and lenses
• Focal points of mirrors, spherical surfaces, thin lenses
• Focal points and principal planes for thick lenses
 Comparison to theory:
•
•
•
•
Spherical mirror equation
Relation for single spherical surface
Lens maker’s formula (thin lenses)
Equations for focal length and principal planes (thick lenses)
 Practicing:
• Sign conventions for radii and focal points of curved reflecting and
refracting surfaces.
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
The principle of finding a focal point
Incoming parallel light rays
Exiting light rays
Reflecting or
refracting
object
Focal point
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
The principle of finding a focal point
Incoming parallel light rays
Exiting light rays
Reflecting or
refracting
object
Focal point
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Determination of the radius of a spherical mirror
Concave mirror, reflecting side here.
1
D2 

R   x 
2
4x 
R
x
D
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
…alternative method…
Polar graph
paper
Move mirror until
curvature matches
the curvature on
polar graph paper.
then measure R
as shown.
R
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Convex versus concave
Concave Mirror:
Convex Mirror:
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Convex versus concave
Concave Lens:
Convex Lens:
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Convex versus concave
Plano Concave Lens:
Plano Convex Lens:
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Convex versus concave
Convex Concave Lens:
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
The Spherical Mirror Equation
1 1
2 1
  
s0 si
R f
So: object distance
Si: image distance
R: radius of curvature of spherical mirror
f: focal length of spherical mirror
Sign Convention for Spherical Mirrors
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Sign
so
si
f
R
yo
yi
+
-
Left of V, real object
Left of V, real image
Concave mirror
C right of V, convex
Above axis, erect object
Above axis, erect image
Right of V, virtual object
Right of V, virtual image
Convex mirror
C left of V, concave
Below axis, inverted object
Below axis, inverted image
Sign Convention for Mirrors
S
C
P
F
V
f
si
R
so
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Refraction on a single spherical surface
n1
n2
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Single Spherical Surface
n1 n2 n2  n1
 
so si
R

n1 n2 n2  n1


f1 f 2
R
n1: index of refraction on one side of the surface
n2: index of refraction on the other side of the surface
R: radius of curvature of the surface
f1 : focal distance in first medium
f2 : focal distance in second medium
so : object distance
si : image distance
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Determining the two focal distances for a spherical surface
Fo
V
Note that Hecht names f1
and f2 differently:
Instead of f1 he used fo as
in “object focal distance”
fo
Instead of f2 he uses fi as
in “image focal distance”
V
C
fi
Fi
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Sign Conventions (according to Hecht)
Sign Convention for Spherical Refracting Surfaces
and Thin Lenses (Light Entering from the Left)
Fo
so , fo
xo
si , fi
xi
R
yo , yi
V
fo
C
V
Fi
fi
fi
+
+
+
+
+
+
left of V
left of Fo
right of V
right of Fi
if C is right of V
above the optical
axis
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Practical way of making a single spherical surface
Focus still in
the plastic
Semi-circular plastic
Rectangular plastic
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Lens Maker’s Equation (for thin lenses)
 1
1
1 
 ( n  1)  
f
 R1 R2 
Use proper conventions:
R is positive if center of curvature (C) is to the right of vertex (V)
R is negative if center of curvature (C) is to the left of vertex (V)
R1 is the curvature on the left side.
R2 is the curvature on the right side.
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Examples
 1
1
1 

 ( n  1)  
f
 R1 R2 
C1
V1
V2 C2
R1 negative
(C1 to the
left of V1)
 f is negative
R2 positive
(C2 to the
right of V2)
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Examples
 1
1
1 

 ( n  1)  
f
 R1 R2 
C1
C2
V1
R1 positive
(C1 to the
right of V1)
 f is positive
V2
R2 negative
(C2 to the
left of V2)
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Thick Lenses: Measuring focal distances and principal planes
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Thick Lenses: Measuring focal distances and principal planes
Modern Optics Lab
Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
Thick Lens Equations:
You can now use simple lens equations as long as all distances are
measured from the principal planes instead of the center of the lens.