SLIDE 1 Geometrical Optics I: I: refraction, , reflection, , le lenses and im image formation
Humberto Cabrera
Venezuelan Institute for Scientific Research International Centre for Theoretical Physics
Preparatory School to the Winter College on Optics: Advanced Optical Techniques for Bio-imaging
SLIDE 2
Basi asic components and nd th their ir fu functions What is is in insi side?
Refraction, reflection, lenses, and image formation
SLIDE 3 Topics:
rtie ies o lig light 2. . Lig ight matter in interactio ion 3. . Refr fractio ion and refl flectio
fractiv ive len lenses 4. . Im Image form rmatio ion
SLIDE 4
Propertie ies of lig light. . Ele lectromagnetic ic spectrum
SLIDE 5
Ele lectromagnetic ic spectrum and tis issue absorption
SLIDE 6 Propertie ies of lig light. . Waves
am ampli litude E wavelength (λ) frequency (ν) speed (c) phas ase (ϕ) pola
intensity (I)
λν = c
SLIDE 7
Wavelength: λ=635 nm Power: P=2 mW Spot (area): A=8 mm Speed: c=3.00×108 m/s Area: A=8 mm2 ε0 = 8.854 187 817... × 10−12 F⋅m I=P/A=250 W/m2 E=430 V/m Spot (area) =8 mm Speed (c)=3.00×108 m/s ν =5x1014 Hz
Propertie ies of lig light. . Waves
SLIDE 8
Propertie ies of lig light. . Speed
n=1 n>1 n=1
SLIDE 9 Propertie ies of lig light. . Rays and wavefronts
(To simplify drawing light, rays and wavefronts are used instead)
SLIDE 10
Light matter interaction. Refraction and reflection
SLIDE 11
Lig ight matter in interaction. . Snell ll´s la law
SLIDE 12
Lig ight matter in interaction. . Fresnel l equations for normal l in incid idence
~4 ~4% for air air-glass ~96% for air-glass
SLIDE 13 Refractiv ive le lenses. . Focusing
where n is the index of refraction of the lens material, and R1 and R2 are the radii of curvature
- f the two surfaces. For a thin lens, d is much
smaller than one of the radii of curvature (either R1 or R2) Lens maker´s equation:
SLIDE 14
Refractiv ive le lenses. . Lens shapes
SLIDE 15
Refractiv ive le lenses. . Focus siz ize
Is the focus really a point?, No, the focus has a size proportional to the wavelength Airy disk
SLIDE 16
Refractive lenses. Aberrations
SLIDE 17 Refractive lenses. Ray tracing
- 1. Any ray that enters parallel to the axis on one side of the lens proceeds towards
the focal point f on the other side
- 2. Any ray that arrives at the lens after passing through the focal point on the front
side, comes out parallel to the axis on the other side
- 3. Any ray that passes through the center of the lens will not change its direction
SLIDE 18
- By tracing these rays, the relationship between the object distance and the
image distance can be shown to be (thin lens equation):
Refractive lenses. Ray tracing
𝟐 𝑻𝟐 + 𝟐 𝑻𝟑 = 𝟐 𝒈
- With ray tracing rules 1, 2 and 3, the position and size of an image can be
determined from the position and size of an object
𝑵 = − 𝑻𝟑 𝑻𝟐 = 𝒊𝟑 𝒊𝟐
- And the magnification of the image:
SLIDE 19 https://www.youtube.com/watch?v=OSUGRvYwxw8
SLIDE 20 https://www.youtube.com/watch?v=mfytZxM8lho
Image formation: Real and virtual images
