∵BIO Predict/Calculate Optical Activity Optically active...

$\because$ BIO Predict/Calculate Optical Activity Optically active molecules have the property of rotating the direction of polarization of linearly polarized light. Many biologically important molecules have this property, some causing a counterclockwise rotation (negative rotation angle), others causing a clockwise rotation (positive rotation angle). For example, a 5.00 gram per 100 mL solution of l-leucine causes a rotation of $-0.550^{\circ}$ ; the same concentration of $d$ -glutamic acid causes a rotation of $0.620^{\circ} .$ (a) If placed between crossed polarizers, which of these solutions transmits the greater intensity? Explain. (b) Find the transmitted intensity for each of these solutions when placed between crossed polarizers. The incident beam is unpolarized and has an intensity of 12.5 $\mathrm{W} / \mathrm{m}^{2}$ .

$\because$ BIO Predict/Calculate Optical Activity Optically active molecules
have the property of rotating the direction of polarization of linearly
polarized light. Many biologically important molecules have this
property, some causing a counterclockwise rotation (negative rotation angle), others causing a clockwise rotation (positive rotation
angle). For example, a 5.00 gram per 100 mL solution of l-leucine
causes a rotation of $-0.550^{\circ}$ ; the same concentration of $d$ -glutamic
acid causes a rotation of $0.620^{\circ} .$ (a) If placed between crossed polarizers, which of these solutions transmits the greater intensity?
Explain. (b) Find the transmitted intensity for each of these solutions when placed between crossed polarizers. The incident beam is
unpolarized and has an intensity of 12.5 $\mathrm{W} / \mathrm{m}^{2}$ .

Key Concepts

Malus's Law

Malus's Law is a fundamental principle that quantifies the intensity of polarized light after passing through a polarizer. The law states that the transmitted intensity is proportional to the square of the cosine of the angle between the light's polarization direction and the axis of the polarizer. This law is essential for calculating the final intensity of light after it is altered by an optically active substance and subsequently filtered through a second polarizer.

Polarization of Light

Polarization describes the orientation of the oscillations of the electric field vector in a light wave. Unpolarized light, consisting of waves oscillating in all possible directions perpendicular to the propagation direction, can become partially or fully polarized when passed through certain materials or polarizing filters. The polarization state is critical in understanding how light interacts with optical devices and crystals.

Optical Activity

Optical activity refers to the property of certain substances to rotate the plane of linearly polarized light. This phenomenon is commonly observed in chiral molecules, which have non-superimposable mirror images. The direction and magnitude of the rotation depend on the nature of the chiral compound, its concentration, and the path length of the light through the medium.

Crossed Polarizers

Crossed polarizers are a pair of polarizing filters arranged so that their polarization axes are perpendicular to each other. In this configuration, ideally no light should pass through one filter after it has passed through the other. When a sample that rotates the plane of polarized light is placed between them, the rotation allows some light to pass through the second polarizer, and the transmitted intensity is indicative of the rotation angle.

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