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Dispersing properties of Prism and optical activity in solutions

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Dispersion

• The dependence of wave speed and index of refraction on wavelength is called dispersion.

• Therefore the index of refraction of a material depends on wavelength.

• n decreases with increasing wavelength and decreasing frequency

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wavelength in the material is given by

λ = λ0 /namount of dispersion is

large in silicate flint glass

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prism

• prism is a transparent optical element with flat, polished surfaces that refract light.• A prism can serve as a dispersive element, a beam splitter and a polarizing device.

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History

• On February 6, 1672, Newton presented a classic theory at royal academy

of London in his book opticks• He concluded that white light consisted of a mixture of various colors.

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𝜃 𝑖2𝜃 𝑡 1𝜃 𝑖 𝜃 𝑡 2

𝛿

Ray diagram

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derivation

t1+ A1 + 90 = 180

i2+ A2 +90 = 180

(t1 +i2) + A1 + A2 =180o (1)

A1+ A2 + A = 1800(2)

comparing (1) n (2) (i1 +i2) = A = i1 +i2- A

𝛿

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Using snells law n1sin t2 = n2sini2

i2 = sin-1(n2sint2)

i2 = sin-1(n2sin(A- t1))

i2 = sin-1[n2sinA(n2 – sin2i1)1/2 – cos A sin i1]

=i1 + sin-1[n2sinA(n2 – sin2i1)1/2 – sin i1 cos A] -A𝛿

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• Apparently, increases with n. which is itself a function of frequency, so we designate the deviation as (v) or (lambda)𝛿 𝛿

• The smallest value of is known as the minimum deviation. Differentiating Eq. (a) and setting it equal to zero yields

Taking the derivative of Snell's Law at each interface

𝜖 ∀

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• Dividing the last two equations and substituting

using of Snell's Law once again

The value ofi1for which this is true is the one for which = 0Inasmuch as n is not = 1, it follows that

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And therefor

This means that the ray for which the deviation is a minimum traverses the prism symmetrically, that is, parallel to its base.

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Deviation versus incident angle

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45 n = 1.5 40 A = 600

35 30 40 50 60 70 80i1

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Pellin-Broca prism

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Conti..

• a single monochromatic ray of wavelength A traverses the component prism DAE symmetrically

• thereafter to be reflected at 45" from face AB• The ray will then traverse prism CDB

symmetrically, having experienced a total deviation of 90".

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• The ray can be thought of as having passed through an ordinary 60“ prism (DAE combined with CDB) at minimum deviation

• If the prism is now rotated slightly about an axis normal to the paper, the incoming beam will have a new incident angle.

• A different wavelength component, say AZ, will now undergo a minimum deviation, which is again 90"-hence the name constant deviation.

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Abbe prism

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• Refractive index can be used as a base for studying the properties of light and deviation of the light and its components.

• This may also find its application various purposes as in case of cars, satellites, aircrafts, appropriate refractive index of glass for the human eye, glass made utensils and many others.

Applications

Optical activity in liquids

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Optical activity

A substance is optically A substance is optically active if it rotates the plane of polarized light.

In order for a substance to exhibit opticalactivity, one enantiomer must be present in excess of the other

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Introduction

Any material that causes the E-field of an incident linear plane wave to appear to rotate is said to he optically active .The plane-of-vibration appears to have revolved clockwise, the substance is referred to as dextro-rotatory (from the Latin dextro, meaning right). If E appears to have been displaced counterclockwise, the material is levo-rotatory l-rotatory (from the Latin levo,meaning left)

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History

• In 18 1 1 the French physicist Dominique F. J. Arago first observed the phenomenon of optical activity.

• Jean Baptiste Biot (1774-1862) saw this same effect while using both the vaporous and liquid forms of various natural substances. .He for the first time distinguish between right- and left-handed rotation.

• In 1825 Fresnel said that linear wave can be represented as a superposition of R-state and L-states.

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Lactic acid

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Analine

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glucose

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Rotation of plane-polarized light

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Enantiomorphic substance

The substances having same external appearance but internally they are mirror image of each other such substances are enantiomorphs of each other ,these substances are called enantiomorphic substance

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Analytical treatment

Two waves represent R and L state are given by

The final disturbance is given by E=Eocos[(KR+KL)z / 2-ωt][ icos(KR+KL)z /2 +jsin(KR+KL)z / 2]

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Conti…..

• At the position where the wave enters the medium (z = 0) it is linearly polarized along the x-axis, that is

E=Eocos ωt i If• nR > nL or equivalently kR > kL,E will rotate

counterclockwise• kL > kR the rotation is clockwise

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Diagram

Measuring the Optical rotation of compounds

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Polarimetry♦ Polarimetry is the measurement of the polarization of light

♦ Anisotropic crystalline solids, and samples containing an excess of one enantiomer of a chiral molecule, can rotate the orientation of plane-polarized light. Such substances are said to have optical activity.

♦ Measurement of this change in polarization orientation is called polarimetry, and the measuring instrument is called a polarimeter.

♦ These measurements are useful for studying the structure of anisotropic materials, and for checking the purity of chiral mixtures.

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Optical Rotation and Polarimetry

Chiral molecules will rotate polarized light:

monochromatic light source

randomly oriented light

optical polarizer - only allows "vertical" light to pass through

optical polarizer - only allows "horizontal" light to pass through

No light emitted

monochromatic light source

randomly oriented light

optical polarizer - only allows "vertical" light to pass through optical polarizer - only allows "horizontal" light to pass through

chiral material detector

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monochromatic light source

randomly oriented light

optical polarizer - only allows "vertical" light to pass through optical polarizer - only allows "horizontal" light to pass through

chiral material detector

monochromatic light source

randomly oriented light

optical polarizer - only allows "vertical" light to pass through

optical polarizer

chiral materialdetector

The maximum signal will be optained if the second polarizer is rotated to match the light rotation:

maximum signal

Optical Rotation and Polarimetry

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Rotation of plane-polarized light

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Rotation of plane-polarized light

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a

Rotation of plane-polarized light

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The amount of optical rotation is determined by the molecular structure

and concentration of chiral molecules in the substance by Biot’s Law:

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What is a Polarimeter?

♦ Polarimeter is the scientific instrument used to make the polarimetry measurements.

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Schematic of a Polarimeter

The simplest polarimeter consists of a monochromatic light source, a polarizer, a sample cell, a second polarizer, which is called the analyzer, and a light detector.If the analyzer is oriented 90o to the polarizer so that no light reaches the detector.

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Light: electromagnetic radiation

Optical activity is usually measured using light having a wavelength of 589 nm; this is the wavelength of the yellow light from a sodium lamp and is called the D line of sodium.

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Examples

• The direction and magnitude of rotation must be determined experimentally.– There is NO CORRELATION between (R) and (S)

configuration and the direction of rotation.

C

CH3

CH2CH3HHO

C

C

CH3

CH2CH3HHO

HOH

CH3

CH3CH2

(+)-2-butanol (-)-2-butanol+13.5o rotation -13.5o rotation

(S)-(+)-2-butanol (R)-(-)-2-butanol

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Examples

(S)-(-)-thyroxinebiologically activeO CH2

CCO2H

HH2NI I

II

HO

O CH2HO

I

I I

IC

CO2H

NH2H

(R)-(+)-thyroxineinactive

O CH2

CCO2H

HH2NI I

II

HO

O CH2HO

I

I I

IC

CO2H

NH2H

Unlike (R)-(-)-2-butanol, (R)-thyroxine rotates light to the right.

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Polarimetry Aplications

Research and Technological aplications: • Distinguishing between optical isomers • Isolating and identifying unknowns crystallized from various solvents or

separated by high performance liquid chromatography• Monitoring changes in concentration of an optically active component in a

reaction mixture, as in enzymatic cleavage. • Analyzing molecular structure by plotting optical rotatory dispersion curves

over a wide range of wavelengths. • Investigating kinetic reactions by measuring optical rotation as a function of

time.• Liquid crystal displays and polarized sunglasses.• All radio transmitting and receiving antennas are intrinsically polarized, special

use of which is made in radar.• Polarizing filters are used in photography

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Pharmaceutical industry

• Determines product purity by measuring specific rotation and optical rotation of:

· Amino acids

· Amino sugars

·Analgesics

· Antibiotics · Cocaine · Codeine

· Dextrose · Diuretics · Serums

· Steroids •Tranquilizers · Vitamins

Flavor, Fragrance and Essential Oil Industry

Utilizes polarimetry for materials inspection of:

·Camphors

· Citric acid

· Glyceric acid

· Gums · Lavender oil

· Lemon oil

· Orange oil

·Spearmint oil

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Food Industry

Ensures product quality by measuring the concentration and purity of the following compounds in sugar based foods, cereals and syrups:

·Carbohydrates

·Fructose

·Glucose

· Lactose ·Levulose

·Maltose

· Raffinose ·Sucrose ·

Xylose

· Various Starches

· Natural mono-saccharides

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Chemical Industry

• Analyzes optical rotation as a means of identifying and characterizing:

Biology:

· Biopolymers · Natural polymers · Synthetic

polymers

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Medicine

• Research of glucose in urine - Diabetes Mellitus

• Research of albumin in urine - Renal diseases

• Hormone research Analysis of: -steroid hormon -testosterone Enzymology and toxicology research.

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