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Lenses - Advanced Analytical Chemistry - Lecture Slides, Slides of Analytical Chemistry

Lakshmibai National Institute of Physical Education Analytical Chemistry

Indicator Electrodes, Potentiometry, Electrochemistry, Electrode Kinetics, Electrogravimetry, Polarography, Square Wave Voltammetry, Wavelength Selection, Types of Spectroscopy, Detectors, Theory of Molecular Absorption, Absorption by Organic Molecules, Applying UV-vis Spectroscopy are major topics of this course. Main points from these slides are: Lenses, Focal Length, Lens Material, Radius of Curvature, Lens Equation, Refractive Index, Monochromator, Mirrors, Astigmatism, Numerical Aperture

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Lenses – lens equation (for a thin lens)

1 1 1

---- = (η–η’) ------ - ------

f r1r2

Where f = focal length

η= refractive index of lens material

η’ = refractive index of adjacent material

r1= radius of curvature of first surface

r2= radius of curvature of second surface

1 1 1

---- = ---- - ----

f i o

object

image

ofi

distance

to image

distance

to object

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Lenses

– lens equation (for a thin lens)

f

r

Where

η f = focal length (^) = refractive index of lens material

η ’ = refractive index of adjacent material

r 1 (^) = radius of curvature of first surface

r 2 (^) = radius of curvature of second surface

object

image

to imagedistance

to objectdistance

Focal length

is important specification of a

monochromator

focal length (f)

f/ (f number) = ------------------------------

lens clear aperature

• Light gathering power ~ 1/(f/)• Larger f/ means getting less light• f/ is measure of light gathering power

or focal length)at f (focal pointPoint source

beamsParallel

Mirror problem

spherical aberrations – f gets

problem for lenses also)shorter as rays go off axis (this can actually be a

Several solutions:

Just use center of mirror (or lens) – but this

reduces the light-gathering power (f/ increases)

Use parabolic mirror (harder to make

Use Schmidt Corrector

distorts light beams good focusso they come to a

MirrorSpherical

Astigmatism

– for an object off axis, the

two images displaced from each otherhorizontal and vertical focuses differ – get

Numerical Aperture

(NA) = sin

device accepts light angle over which a

Slits

– entrance and exit slits

Decrease slit widthSlits affect energy throughput & resolution

gain resolution & lose

energy throughput

Open slits wider

increase signal

(throughput) but lose resolution

Light exiting a monochromator exit slit has a

triangular distribution

Optical Efficiency

= throughput x resolution

Good criterion for comparing optical systems

Prism

Grating

Interferometer

Monochromator

powerRelative

λ o +10 +

Range of

(^) λ ’s passing

when set at

(^) λ o

or spectral slit widthbandpass or bandwidth

Dispersion Devices

Prisms

Light bends due to

ff ff

λ )

d θ d θ d η

Angular Dispersion = ----- = ------ x ------

d λ d η d λ

Angle changes with

λ (^)

the larger the better

b A

b = base length A = apical angle

(i.e. angle A)prism designfunction of

materialof prismfunction

Dispersion Devices

1) Prisms

d η

----- depends on material, ----- greatest at shorter

d λ

b A

b = base length A = apical angle

d θ

Linear Dispersion

nm------ = f -----

d λ

For constant bandwidth, slit widths must be varied Depends on angular dispersion and focal length

with

λ to compensate for variations in d

η / d

Stated another way, linear dispersion changes in

different regions of the spectrum

Problem with quartz prisms is that quartz is

both directions and this effect is eliminated.the light travels essentially the same path inthe Littrow prism or any reflecting prism,optically active (optically anisotropic). With

Cornu Prism

Right handed quartz

quartzLeft handed

(-)

(+)

f/ of a monochromator is important if have a

smallest f/ sets the overall f/ for the system.weak source. For lenses in series, the

Lens Summary:

length depends on2) can have chromatic aberrations = focal1) rugged, easy to use, inexpensive

which varies with

composite glasses sosolution is to fabricate lenses out of a

is constant with

to reflection3) Each lens results in some light loss dueThis increases cost

Gratings

based on diffraction & interference

Transmission Gratings & Reflection Gratings

or a mirror (usual kind)consist of a series of grooves in glass or quartz

Radiation Monochromatic