Download Spherical Refracting Surfaces and Image Formation and more Slides Electrical Engineering in PDF only on Docsity!
LECTURE 25: Spherical Refracting Surfaces
4/16/12 2
Previous Lecture: Geometric Optics
In situations in which the length scales are >> than
the light’s wavelength, light propagates as rays
incident
ray
reflected
^ ray
1!^ r
n 1
refracted
ray
2^ n^2
Reflection:
Refraction:
θ i =θ r
n 1 sin θ 1 = n 2 sin θ 2
If n 1 > n 2 then 2 > 1
If n 2 > n 1 then 1 > 2
Refracted ray bends away from normal
Refracted ray bends toward the normal
4/16/12 3
Spherically Refracting Surfaces
4/16/12 4
Spherically Refracting Surfaces
4/16/12 5
Spherically Refracting Surfaces
4/16/12 6
Summary: Spherically Refracting Surfaces
1. Real Images form on the side of a refracting surface that is
opposite the object.
2. Virtual Images form on the same side as the object
3. For light rays making only small angles with the central axis:
4. When the object faces a convex refracting surface, the radius
of curvature is positive.
5. When object faces a concave surface, radius of curvature is
negative.
n 1
s
n 2
s '
n 2 − n 1
r
4/16/12 7
Example: Mosquito in Amber
A mosquito is embedded in amber
with an index of refraction of 1.6. One
surface of the amber is spherically
convex with a radius of curvature 3.
mm. The mosquito head happens to
be on the central axis of that surface,
and when viewed along the axis
appears to be buried 5.0 mm into the
amber. How deep is it really?
Draw Picture
4/16/12 8
Example: Mosquito in Amber
4/16/12 13 Images from Thin Lenses 4/16/12 14 Images from Thin Lenses 4/16/12 15 Locating Images by Drawing Rays
- Ray initially parallel to central axis will pass through F 2.
- Ray passing through F 1 will emerge parallel to the central axis.
- Ray passing through center of lens will emerge with no change in direction because the ray encounters the two sides of the lens where they are almost parallel.
F 2
F 1
O
I
4/16/12 16 Locating Images by Drawing Rays F 2 F 1
O
I
- Ray initially parallel to central axis will pass through F 2.
- Backward extension of ray 2 passes through F 1
- Ray 3 passes through center of lens will emerge with no change in direction.
4/16/12 17 Locating Images by Drawing Rays F 2 F 1 3
O
I
- Backward extension of ray 1 passes through F 2
- Extension of ray 2 passes through F 1
- Ray 3 passes through center of lens will emerge with no change in direction.
4/16/12 18 Two Lens System Lens 1^ Lens 2 O s 1
- Let s 1 represent distance from object, O, to lens 1. Find s 1 ’ using: 1 f 1 = 1 s 1 + 1 s 1 '
- Ignore lens 1. Treat Image 1 as O for lens 2. Use s 2 = s 1 ’. 1 f 2 = 1 s 2
1 s 2 ' M = m 1 m 2 = − s 1 ' s 1 ⎛ ⎝⎜ ⎞ ⎠⎟ − s 2 ' s 2 ⎛ ⎝⎜ ⎞ ⎠⎟
- Overall magnification: Note: If image 1 is located beyond lens 2, s 2 for lens 2 is negative. 4/16/12 19 Example: Two Lens System A seed is placed in front of two thin symmetrical coaxial lenses (lens 1 & lens 2) with focal lengths f 1 =+24 cm & f 2 = +9.0 cm, with a lens separation of L=10.0 cm. The seed is 6.0 cm from lens 1. Where is the image of the seed? Lens 1: Lens 2: Treat image 1 as O 2 for lens 2. O 2 is outside the focal point of lens 2. So, image 2 will be real & inverted on the other side of lens 2.
