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

http://www.ophysics.com/l12.html

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

http://www.ophysics.com/l16.html

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