Optics Applications
M. Rocha
Physics 2B
Geometric Optics, The Eye, Microscopes and Telescopes
Lenses (Refraction)
Direction of Refraction
Waves bend towards the normal when going from fast to slow
and
away from the normal when going from slow to fast
L = \theta \times r
Small angle approximation
Arc Length = Angle in radians x Radius
r \sin \theta \approx r \ \theta
\approx
r = Hypotenuse
Adjacent
Arc Length and The Small Angle Approximation
r
Oposite =
r \sin \theta
Oposite
L
\approx
\Rightarrow \sin \theta \approx \theta
Lenses
Curved surface of a convex lens causes light rays to converge, magnifying images
Convex Lenses
Curved surface of a concave lens causes light rays to diverge, shrinking images
Concave Lenses
Lenses
Focal Length
Thin Lens Equation
Virtual vs. Real Images in Convex Lenses
Real Image
Virtual Image
Virtual Images in Concave Lenses
Virtual Images
Checkpoint
o = 10cm
i = 30cm
What is the focal length of the lens in the system below?
f = 7.5 cm
f = \frac{1}{\frac{1}{o} + \frac{1}{i}} = \frac{1}{\frac{1}{10 \ cm} + \frac{1}{30 \ cm}} = \frac{1 \ cm}{ 0.1 + 0.033} = 7.5 \ cm
Checkpoint
If we move the light source (object) to a position 2.5 cm from the lens, in the same setup of the previous checkpoint, what would be the magnification?
f = 7.5 cm
i = \frac{1}{\frac{1}{f} - \frac{1}{o}} = \frac{1}{\frac{1}{7.5 \ cm} - \frac{1}{2.5 \ cm}} = \frac{1 \ cm}{(\frac{-2}{7.5})} = -3.75 \ cm
M = \frac{-i}{o} = \frac{-(-3.75 \ cm)}{2.5 \ cm} = 1.5
Checkpoint
Repeat the previous checkpoint now for a Convex lens?
f = -7.5 cm, O = 2.5, i = ?, M = ?
i = \frac{1}{\frac{1}{f} - \frac{1}{o}} = \frac{1}{\frac{1}{-7.5 \ cm} - \frac{1}{2.5 \ cm}} = \frac{1 \ cm}{(\frac{-4}{7.5})} = -1.88 \ cm
M = \frac{-i}{o} = \frac{-(-1.88 \ cm)}{2.5 \ cm} = 0.75
Mirrors (Reflection)
Law of Reflection
The angle of incidence equals the angle of reflection
Mirrors
Mirrors are the result of specular reflection
Tracing light rays from original, to mirror, to eye allows us to construct the image
Convex Mirrors
Image from convex mirror is smaller and closer than original
Concave Mirrors
Image from concave mirror is larger and farther than original if object close to mirror
Concave Mirror Image
O > f (object outside focal length)
Concave Mirror Image
O < f (object inside focal length)
Covex Mirror Image
f < 0 (always virtual image)
Virtual vs. Real Images in Mirrors
Real Image
Virtual Image
The Eye
Physics of the Eye
Vision Correction
(nearsighted)
(farsighted)
Vision Correction
Myopia Correction
Hyperopia Correction
Microscopes
Total Magnification:
Telescopes
Telescope Magnification
M = \frac{\beta}{\alpha} = \frac{\frac{h}{f_e}}{\frac{h}{f_o}} = \frac{f_o}{f_e}
M = \frac{f_o}{f_e}
h
Telescope Magnification
M = \frac{\mathrm{Telescope \ Focal \ Lenght}}{\mathrm{Eyepice \ Focal \ Lenght}}
Text
Checkpoint
If a telescope has a focal length of 1200 mm. What is the magnification when using a 25 mm eyepiece?
M = 1200 mm/ 25 mm = 48
M = \frac{\mathrm{Telescope \ Focal \ Lenght}}{\mathrm{Eyepice \ Focal \ Lenght}}
Telescopes are Light Buckets
The main purpose of telescopes is to collect as much light as possible while maintaining as much detail as possible
Both the light gathering power and resolution of a telescope increases with the diameter/area of the telescope
Refractors vs. Reflectors
There are two ways to collect light in a telescope. By refraction or by reflection
Refracting telescopes use a primary/objective lens to collect light by refraction
Reflecting telescopes use a primary/objective mirror to collect light by reflection
Refracting Telescopes
Refracting telescopes have many disadvantages:
- The become too long for not that much light collecting area
- Large lenses are extremely expensive to fabricate
- A large lens will sag in the center since it can only be supported on the edges
- Dispersion causes images to have colored fringes
Refraction of light is frequency dependent
This is because higher frequencies travel slower inside the prism
Slowest
Fastest
Refracting Telescopes Suffer from Chromatic Aberration
Slowest
Fastest
Refracting Telescopes Suffer from Chromatic Aberration
Reflecting Telescopes
Reflecting telescopes use a parabolic primary mirror to collect light. Light is focused in front of the mirror, how you observed it without blocking the incoming light?
Reflecting Telescopes
Reflecting telescopes use either detectors or secondary mirrors to gather or re-direct the focused light from the primary mirror
Concave Mirrors
We use concave mirrors to build telescopes in order to focus the light to the detector
Telescope Instruments
Cameras and Charged Coupled Devices (CCDs)
Spectrographs
The End
Optics Applications - Physics 2B
By Miguel Rocha
Optics Applications - Physics 2B
Physics 1 - Week 12-13 - Chapters 28-29
