A PC BASED POLARIMETER BASED ON MALUS ¹ LAW

Application Number:

Name Of Applicant: K.Muralidhara Reddy & Dr. C. Nagaraja

Title of Invention.

Malus' polarimeter (PC based polarimeter based on Malus' law)

Prior Art

PC based polarimeters can also be called as "automatic recording polarimeters". All the present PC based polarimeters are made using the electro/magneto optic modulation techniques. We made the PC based polarimeter with out using the above principles. We made it using the principle of Malus. No PC based polarimeter is made using this principle of Malus' law.

Advantages:

1. Simple Hardware and design due to the Malus' law.

2. Hence the cost of the instrument reduces.

Summary of the Invention:

The main object of the invention is to develop the PC based Polarimeter based on Malus principle, which is simple and cost effective with high accuracy.

Brief description of drawings:

Fig-1 a, b illustrates polarimeter using Malus' law

Fig 2 illustrates optical system for PC based polarimeter

Fig 3 illustrates Dextro/ Laevo graph

Fig 4 a, b, c, d illustrates determination of Dextro/Laevo

Fig 5 illustrates photograph of PC based polarimeter optical set up,

Fig 6 illustrates block diagram of hardware of PC based polarimeter

Detailed description of present invention.

PRINCIPLE AND CONSTRUCTION OF THE PC BASED POLARIMETER BASED ON MALUS' LAW

A. Principle and working of Polarimeter based on Malus' law

Malus' law states that I = \- _\ cos ² θ where h is the intensity of linearly polarized light before the analyzer and I is the intensity after passing the analyzer and θ is the angle between the plane of the vibration and the axis of analyzer. A Polarimeter, to measure the rotation of light through an optically active substance can be designed using Malus' law as follows As shown in Fig 1a the polarizer and analyzer are arranged on a common axis so that their transmission axes are parallel. Now, an un polarized light is allowed to fall on the polarizer. The emerging beam is linearly "polarized and its intensity is equal to half the intensity of incident un polarized light. Now the plane polarized light next passes through the analyzer. Since the transmission axis of the analyzer is parallel to this wave, it passes without any obstruction and its intensity \ = \^.

An optically active substance is placed between the polarizer and analyzer as shown in Fig 1 b. This rotates the plane of vibration of linearly polarized beam that is passing through optically active substance. Hence, the plane of vibration of the emerging beam from optically active substance will be rotated. Hence it is no more parallel to the transmission axis of analyzer but makes an angle of θ as shown in Fig 1 b.

According to Malus' law, the intensity of emerging beam from the analyzer is I = li cos ² θ, where \i is the intensity of beam before falling on the analyzer and li after the analyzer and θ is the angle of rotation of plane polarized light made with transmission axes. If the values of I and h are substituted in the above equation, θ can be evaluated directly.

S. Design of optical system for PC based polarimeter

Fig 2 shows the complete optical system for Polarimeter using Malus' law.

The narrow slit is illuminated by a halogen lamp(S) of 24V, 100W and a collimating lens (Piano convex lens) is situated at a distance equal to its focal length from the slit which sends out a collimated beam of light. Now this parallel white light beam is allowed to fall on an interference filter of 589 nm. All standard samples have been standardized against 589 nm light source. Hence to obtain easy calibration of the instrument it is preferred to use 589nm. Also the standard specific rotation values of the samples are given with reference to 589nm.

After the filter, the unpolarized light falls on the polarizer (P) which linearly polarizes the beam. The polarizer used here is Glan- Thompson prism. It consists of two right-angled calcite prisms that are cemented using Canada balsam together by their long faces. The optical axes of the calcite crystals

are parallel and aligned perpendicular to the plane of reflection. Birefringence splits light entering the prism into two rays, experiencing different refractive indices; the p-polarized o-ray is totally internally reflected ,from the calcite- cement interface, leaving the s-polarized e-ray to be transmitted The Glan Thompson calcite polarizers offer the widest field of view of the calcite polarizers while maintaining a high extinction ratio. Now this plane polarized beam passes through a sample tube (ST) which contains an optically active substance. The polarized beam will be rotated by the sample. After the sample tube, a beam splitteri (BS1) is arranged such that it reflects 50% of the incident light in 90° and allows 50% of the light in straight path. Again this straight light from BS1 falls on a second beam splitter (BS2), which reflects 50% of the incident light in 90° and allows another 50% in the straight path. The light beam reflected in 90° at the beam splitteri is allowed to fall on the analyzer A2. After the analyzer A2, with out any gap a photo sensor S2 is arranged to measure the light intensity. Similarly, the light beam which is reflected in 90° at the beam splitter2 is allowed to fall on photc sensor S3. The light coming in the straight path from beam splitter2 is allowed to fall on the analyzer A1 and after this with out any gap a photo sensor S1 is arranged Hence the light after passing through the sample tube is equally divided in to four branches. The beam splitters used in our polarimeter are 50:50 non- polarizing beam splitter cubes. These cubes provide a 50/50 splitting ratio that is nearly independent of the polarization of the incident light. The entire setup is inserted in a Gl tube of 1 inch diameter. The internal portion of the tube is painted with dull finish black to absorb the internal reflections of the light.

Here the most important design aspect is to keep the distances as BS1.A2=BS1.BS2=BS2.S3=BS2.A1 , so that any changes in the light intensity will equally appear for all four branches in to which the light is divided after the sample tube. Any disturbance to the above condition will seriously affect the accuracy of the instrument.

C. Working of PC based polarimeter

First the sample tube, analyzer A1 and analyzer A2 are removed. Then switch on the light source. Parallel beam of white light is filtered by the interference filter and only 589nm wavelength of unpolarized light is allowed. After passing through the polarizer, the unpolarized beam will be converted in to a plane polarized beam and it is divided into two equal parts at the beam splitteri . 50% of the incident light passes straightly and the remaining 50% of the incident light is reflected and falls on the photo sensor S2. The straight light from BS1 is again equally divided into two parts at the beam splitter2. One part (50%) passes straightly and falls on the photo εensor (SI) and the remaining part (50%) falls on the photo sensor S3. Therefore the intensity of S2 = S1 +S3 and also S1 = S3. The positions of S1 , S2, and S3 are adjusted so that the above relation should be valid. Once this setting is made, until the instrument is not disturbed, there will be no need to make the above adjustment for every measurement. These positions of S1 , S2 and S3 are marked. Then S1 , S2 are removed and analyzer A1 is inserted in the place of . S1 and analyzer A2 is inserted in the place of S2. After the analyzers A1 and A2, now sensors S1 and S2 are placed such that there should be no gap between the analyzers and the sensors. If there exist any gap, S1 and S2

record less intensity which gives error in the readings. Hence accuracy of the instrument will be reduced.

Now without inserting the sample tube, S1 value (I) is measured and this is equal to I ₁ (refer Fig 1a). Since no optical rotation is there, I ₁ without any hindrance passes through analyzer A1 (I ₁ and analyzeri are parallel), and therefore I ₁ = I (S1 value). This value is stored. Now the' sample tube is inserted with an optically active substance. This will now rotate the polarized light I ₁ by θ. And also the solution absorbs I ₁ according to Beer's law and Lambert's law. Now the intensity of the light before the analyzer A1 is not U but it is less than I ₁ . Since the light at BS2 is equally divided to S1 and S3, now S3 also reduces. But S3 value is always maintained to a constant value by an automatic intensity control. Now this circuit increases the intensity of the light source so that again S3 retains its value. This implies the intensity of light before the analyzer A1 comes to normal value I ₁ . Thus, irrespective of the sample and its absorption, I ₁ before the analyzer A2 is maintained to the constant value using S3 and automatic intensity control. >

Now the rotated h falls on the analyzer A2 at an angle θ to its transmission axis. Therefore, from Malus' law the intensity after A2 = I = I ₁ cos ² θ, where I can be directly measured on S1 and I ₁ is already a fixed value. Hence substituting I and I ₁ we can find the optical rotation θ from 0° to 90°. The optical path length of sample tube is 10 cm. The end windows of the sample tube are made from highly annealed strain free crown glass (BSC glass) which is optically inert and therefore does not produce any rotation.

D. Determination of Dextro/Laevo

To determine the Dextro and Laevo nature of the optically active substances, we developed a novel technique named "Dextro/Laevo graph" in which analyzer A2 is employed as follows.

The sample tube is removed. Now the plane polarized light is not rotated. 50% of its intensity is reflected at BS1 on to the analyzer A2. The position of the analyzer A2 is adjusted parallel, 45°, 90°, and 135° to the plane of vibration of polarized beam and the intensity of light is measured after the analyzer A2 using S2 for above positions and these values are stored. The intensities I ₂ versus θ at A2 are drawn and the curve appears as shown in the Fig 3. The I ₂ values between 0° and 45° are named as "D-region" and the values between 45° and 135° are named as "L-region" and the entire curve shown in Fig 3 is named as "Dextro/Laevo graph".

Now the analyzer A2 is fixed at 45 ^° in the clockwise direction to the plane of vibration of polarized light without sample. Now the sample tube is inserted and let the light after passing the sample is rotated by 20 ^c in the clockwise direction (Dextro). Since A2 is already at 45°, now the effective angle between plane of vibration of the light and transmission axis of A2 is 45°-20 ^° = 25 ^° (Fig 4a). The intensity I ₂ is measured and it is I ₂ at 25°. This value falls in D- region as shown in the Fig 3.

Let θ = 70° in the clockwise. Since A2 is already at 45 ^° , again the effective value = 45 ^° -70° = 35° (Fig 4b). The intensity I ₂ is measured at 35° and it falls in the D- region (Fig3). Therefore, it can be concluded that all the rightward rotations between 0° and 90° make the effective angles between 0° to 45 ^° with

A2 and then all fall in the D- region of the graph (Fig 3).

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Let the polarized light be rotated in the anti clockwise direction (towards left) by an angle of 20 ^° . Since A2 is already at 45 ^° in clockwise, the effective angle is 20 ^° + 45° = 65° as shown in the Fig 4c. The intensity I ₂ is measured and it is I2 at 65°and this value falls in L - region of the graph (Fig 3).

Similarly, let the light is rotated to the left by an angle of 70° and the effective angle is 70 ^° +45° = 115° as shown in the Fig 4d. This intensity I ₂ is measured. It is I ₂ at 115 ^° and this value falls in L - region of the graph (Fig 3).

Therefore, it can be concluded that all the leftward rotations between 0 ^° and 90 ^° make the effective angles between 45° and 135° with A2 and then all fall in the L - region of the graph (Fig 3) . After the optical rotation, the I ₂ value is measured and it is compared with above graph values.

Note that when no rotation takes place then the effective angle = 45°. This rotation is determined from the angle measurement from SI sensor. When the θ = 0° implies no rotation. So, every time this should be verified.

This is how the Dextro and Laevo rotation is determined based on "Dextro/Laevo graph" in the range (-90° +90°). After reading the values of I ₂ at 0°, 45 ^° , 90° and at 130°, these values are stored and S2 position is fixed to 45° permanently. Until this position is not disturbed, there is no need to rotate the analyzer A2 every time. Note that the plane polarized light reaches S2 after reflecting from the beam splitter BS1. Hence, from the properties of reflection, the left rotation (Laevo) of the plane of vibration of light will be converted in to right rotation (Dextro) and vice versa.

This comparison of light intensities (measured after the 45° analyzer) with "Dextro/Laevo graph" is able to produce the information of Dextro/Laevo

nature of the sample. This is a unique and a novel technique which makes the above polarimeter as a novel instrument.

Storing the values of h = I (reading of S1 with out sample), calculation of optical rotation (θ) from I = I ₁ cos ² θ, and maintaining the intensity of h as constant irrespective of the sample and comparing the S2 readings to the values given in the graph (Fig 3) are executed by PC. Fig 5 shows the photograph of prototype model of optical setup of polarimeter. The Fig 6 shows the complete block diagram of polarimeter based on Malus' law.