Lecture 18- Dispersion and chromatic aberrations Flashcards
What is dispersion ?
the variation in refractive index with the wavelength of light
What are examples of most transparent materials?
(e.g., glasses, liquids, plastics, crystals)
What are transparent material described as?
Dielectric materials
What is the common property that dielectric materials share?
they all show an increase in refractive index as the wavelength of light decreases
What happens with the refractive indices of these dielectric materials?
The refractive indices of most transparent materials that are used in optical instruments vary throughout the visible spectrum in approximately the same way
How do we quantify dispersion?
need to introduce spectral lines and materials
What are spectral lines?
discrete wavelengths which are used for the measurement of refractive index and also too quantify the dispersive properties of glass materials
What are spectral lines?
discrete wavelengths which are used for the measurement of refractive index and also too quantify the dispersive properties of glass materials
What does the F line of hydrogen show?
blue light at 486.1nm
What does the C line of hydrogen show?
red
-656.3nm
What does the d line show in helium?
yellow
-587.6nm
What shows in mercury line?
546nm
-green
What shows in the sodium line?
Yellow
589 and 589.6nm
What parameter is important?
refractive index - nd
- which is the refractive index of the corresponding material for the helium d line
What is another important parameter?
Difference in refractive index between the nF- nC
- difference between the F line and C line nm of light of hydrogen material
What is the V value parameter?
-quantifies the change in power in a thin lens as a result of dispersion and -varies about 25 to 65
What are these parameters of?
dispersion parameters for principal material - check powerpoint
Why are these parameters of great practical importance in making optical instrumentation in the description of dispersion and the effects on the optical proeprties of these materials?
- the reason why these particular wavelengths (red blue yellow light) are chosen is because they are easily produced from low pressure discharged lamps and
- they cover the EM spectrum to which the eye is sensitive to
Where is the maximum sensitivity of the eye?
555nm
What happens as a result of changes in Refractive index ?
-going from red to blue light- the properties of optical systems change
How do you calculate the power of a thin lens?
F= (n-1) x (c1-c2)
c1 - curvature of front surface
c2- curvature of back surface
the curvature is just the reciprocal of the radius- so when the radius is very large the curvature is very small.
What is the power of the second surface ?
F2= (1-n)c2
What is the combined power ?
F = F1+F2-(d/n)F1F2
What is the power on assumption that d - 0?
F=(n-1)(c1-c2)
What is the power on assumption that d - 0?
F=(n-1)(c1-c2)
What is the formula used for these changes in refractive index in the wavlelgnths?
F(wavelength)=(n(wavelength)-1)(c1-c2)
Question : Find the focal lengths of a single thin, equiconvex lens for red (nC) and blue (nF) light given that the power of the lens for the helium d-line is +5D. ?
Hence we can calculate a value for the longitudinal chromatic aberration of this lens for a distant object.
- given refractive indices for c,d,f lines of crown glass and dense flint glass
- given power of helium d line
- have dispersion- which causes change in power of lens for helium d line and c,F lines.
5= (1.5169-1)(2c1) - as equiconvex
2c1= 9.67
c1= 4.78 - now use this for F line equation and C line equation - Ff = (nF-1)(2c1)
Answers:
r1 = -r2 = 20.676 cm
f’C = 20.101 cm; f’F = 19.774 cm;
LCA = 3.27 mm
LCA = f’c - f’F
(repeat for dense flint glass)
What do you use if it is a equiconvex lens ?
F=(n-1)(2c1)
so when finding out curvature you then divide by 2.
will an identical lens made from dense flint glass will have greater LCA?
yes
