1. Lecture 2: Basic Astronomical Optics
Prisms, Lenses, and Mirrors

2. Basic Optical Elements
Refraction (Lenses)
No longer used for large telescopes
Widely used for instrument optics
Reflection (mirrors)
Widely used for large telescopes
Dispersion (prisms, grisms, gratings)
Grisms, prisms, and gratings are all used in modern instrumentation
Commonly used for spectrographs
Prisms convey basic concept

3. Snell’s Law ni i r nr
Snell’s Law : ni sin (i) = nr sin (r) ni = index of refraction in incident medium nr = index of refraction in refractive medium i = incident angle r = refractive angle Refraction of the Earth’s atmosphere on stellar light beam and ray bow effect due to the Snell’s law. Refraction is also a key tool in designing astronomical optics.

4. What makes a rainbow? Water droplets act like prisms,
…refracting and reflecting light.
“White” light from the Sun is refracted into colors and reflected.
We see droplets in an arc ~42o away from the direction opposite the Sun.

5. A 40-42 degree arc around this shadow
Many droplets create an arc of reflected light

6. Snell’s Law ni i r nr
Snell’s Law : ni sin (i) = nr sin (r) Values of n for various materials: Vacuum 1 Air (STP) Ice 1.31 Water Table salt 1.54 Crown glass Sapphire 1.77 Diamond In general these values are wavelength-dependent

7. Snell’s Law ni i r nr
Refractive indices for different glasses (wikipedia)

8. Snell’s Law
Snell’s Law : ni sin (i) = nr sin (r) Does light always get transmitted (refracted)? If not, what is the condition for reflection. There’s a critical angle of incidence such that the refracted angle is 90 degrees -- i.e. the refracted ray goes along the surface. Setting r=90, one sees that this is equivalent to sin(i)= nr / ni For larger incident angles, the light is reflected back into the original medium. This is called total internal reflection. Note that internal reflection can only occur in the denser medium (nr < ni). ni i r nr

9. Snell’s Law ni i r nr Snell’s Law : ni sin (i) = nr sin (r)

10. Fiber Light Transmission
Light leak
Total Internal Reflection: n0 n2 n1
Core
Cladding u0 u1 i1
TIR
Fiber Acceptance Cone Angle:
Only incoming beams with incident angles smaller than u0 will pass the fiber without leakage!
The numerical aperture:

11. Snell’s Law: Application to a Prism
Prisms are simple dispersive elements
First surface disperses the light
Second surface disperses further
At this surface different wavelengths also have different angles of incidence
Illustrates the basic idea of dispersion for spectroscopy
wikipedia

12. Dispersing Element 1: Prisms
Deviation angle:
Deviation angle, , depends on refractive index, n, wedge angle, , and incident angle, 1

13. Basic Optical Elements
Refractive Lenses (Convex and Concave
Glass plates and Optical lenses: applied refraction

14. Basic Optical Elements
Refractive Lenses (Convex and Concave)
Convex lenses are converging lenses
Concave lenses diverging lenses
Flipped (opposite) for mirrors
f is defined as the focal length -- the distance from the lens to the focus point.

15. Lenses are shaped to bend light to a focus:
How do lenses work?
Lenses are shaped to bend light to a focus:
The shape can be a parabola

16. Basic Optical Elements
Refractive Lenses (Convex and Concave
Light travelling on-axis doesn’t bend
How would you change the focal length?

17. Basic Optical Elements
Refractive Lenses (Convex and Concave
Light travelling on-axis doesn’t bend
Is the focal length the same for all wavelengths of light?

18. Thick Lenses F P P EFL Cardinal Points and Planes: F FFL BFL P P F
Unprimed are in object space
Primed are in image space
First order optics = Gaussian optics = paraxial optics = perfect optics F
Optical Axis P P
EFL
Cardinal Points and Planes: F
FFL
F Front focal plane/point
F Rear focal plane/point
P Front principal plane/point
P Rear principal plane/point
BFL P P F
EFL: Effective focal length
BFL: Back focal length
FFL: Front focal length

19. Paraxial Image Formation
Newtonian equations: Origins at focal plane h h f f P F F P z z´ h h
Magnification, m = h´/h = f/z = z´/f ´
zz´ = ff´

20. Gaussian equations: Origins at principal planeh h f f P F F P z z´
Magnification, m = h´/h = f/(z-f) = (z´- f ´)/f ´
When f = f

21. Basic Optical Elements
Refractive Lenses (Convex and Concave
Combination of concave and convex lenses can be
used to make a more complex (compound) lens.

22. Lenses Rays parallel to the optical axis will pass through the focus
Rays through the center will be undeviated.
Focal length (f) is distance from lens to focus
Focal ratio (f/ratio or f/number) = f/D, where D is the diameter of the lens
Small f/ratio is considered “fast”, large is “slow”
Power of a lens: P=1/f (units of P are diopters for f in meters)
How does one compute the focal length?
Define R1 and R2 and the radii of curvature for the two sides of the lens:
Lens maker’s formula:
In this example:
R1>0
R2<0
hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenmak.html

23. Lenses Rays parallel to the optical axis will pass through the focus
Rays through the center will be undeviated.
Focal length (f) is distance from lens to focus
Focal ratio (f/ratio or f/number) = f/D, where D is the diameter of the lens
Small f/ratio is considered “fast”, large is “slow”
Power of a lens: P=1/f (units of P are diopters for f in meters)
How does one compute the focal length?
Two thin lenses in contact:
Total focal length is given by: 1/f= 1/f1+1/f2, or P=P1+P2
hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenmak.html

24. Lenses
Of course you can create lenses with various curvatures. In all cases, the lens maker’s formula can still be used to give you the focal length.
wikipedia

25. Lenses
From the basic lens elements we’ve discussed, you can also construct compound lenses for various applications (like cameras). The specific example below shows how two materials with different refractive indices can be coupled to minimize chromatic aberration (unwanted dispersion).
wikipedia

26. Keplerian Refracting Telescope
Objective Lens fo fe
Eyepiece Lens θe θo
Focal point
Angle seen at objective: θo Angle seen at eyepiece: θe
Objective Focal Length: fo Eyepiece Focal Length: fe
The telescope's magnification:
M= θe/ θo=fo/fe

27. Keplerian Refracting Telescope Field of View
Objective Lens fo fe
Eyepiece Lens
Focal point
Field of View

28. Galilean Refracting Telescope
Objective Lens fo
Eyepiece Lens θO θe
Focal point fe
Angle seen at objective: θO Angle seen at eyepiece: θe
Objective Focal Length: fO Eyepiece Focal Length: fe
The telescope's magnification:
M= θe/ θo=fo/fe

29. Mirrors Same concepts of focal length, f-ratio, etc. still apply
Concave mirrors commonly used for telescopes
(We’ll talk about the curvature of these mirrors later.)
van.hep.uiuc.edu/.../ htm

30. Mirrors Same concepts of focal length, f-ratio, etc. still apply
Flat mirrors
Used to redirect light path
“Folding” mirrors are flat
mirrors used to “fold” the
light path
wikipedia

31. Mirrors Two mirrors to form a reflective telescope
Same concepts of focal length, f-ratio, etc. still apply
wikipedia

32. The Cassegrain Telescope
Secondary Mirror
Primary Mirror
Secondary magnification:
Two-mirror systems control aberration, change magnification
Consists of a concave primary and convex secondary
Short tube length
Convenient focal surface
Free of spherical aberration
Off-axis image sharpness depends strongly on the shape of the surfaces
Two popular combinations:
Hyperboloid
Ritchey-Chrétien
Paraboloid
Classical Cassegrain
Secondary
Primary
System