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(D) The optical rotation $	heta$ is directly proportional to the length $l$ of the solution,i.e.,$	heta \propto l$.For the first solution,the rotati

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Right-handed rotation of $3^\circ$

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(D) The optical rotation $	heta$ is directly proportional to the length $l$ of the solution,i.e.,$	heta \propto l$.For the first solution,the rotation per unit length is $\frac{38^\circ}{20 \, cm} = 1.9^\circ/cm$ (right-handed).For the second solution,the rotation per unit length is $\frac{24^\circ}{30 \, cm} = 0.8^\circ/cm$ (left-handed,denoted as $-0.8^\circ/cm$).In a mixture with a volume ratio of $1:2$ in a $30 \, cm$ tube,the lengths occupied are $10 \, cm$ of the first solution and $20 \, cm$ of the second solution.Rotation by the first part: $	heta_1 = 1.9^\circ/cm 	imes 10 \, cm = +19^\circ$.Rotation by the second part: $	heta_2 = -0.8^\circ/cm 	imes 20 \, cm = -16^\circ$.Total rotation: $	heta_{total} = 	heta_1 + 	heta_2 = 19^\circ - 16^\circ = +3^\circ$.$A$ positive value indicates a right-handed rotation.

$A$ $20 \, cm$ length of a certain solution causes right-handed rotation of $38^\circ$. $A$ $30 \, cm$ length of another solution causes left-handed rotation of $24^\circ$. The optical rotation caused by a $30 \, cm$ length of a mixture of the above solutions in the volume ratio $1 : 2$ is:

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