Concept:
Optical rotation of a solution depends on the combined contribution of all optically active species present.
When sucrose undergoes hydrolysis, it splits into two monosaccharides—glucose and fructose—each possessing its own characteristic optical rotation.
Step 1: Nature of sucrose.
Sucrose is dextrorotatory and has a specific rotation of about:
\[
[\alpha]_D \approx +66.5^\circ
\]
Hence, the first part of Statement–I is correct.
Step 2: Effect of hydrolysis of sucrose.
On hydrolysis:
\[
\text{Sucrose} \xrightarrow{\text{hydrolysis}} \text{Glucose} + \text{Fructose}
\]
Specific rotations of the products are:
\[
\text{Glucose: } +52.5^\circ \quad (\text{dextrorotatory})
\]
\[
\text{Fructose: } -92.4^\circ \quad (\text{laevorotatory})
\]
Since the magnitude of laevorotation of fructose exceeds the dextrorotation of glucose, the net rotation of the mixture becomes negative.
Thus, the hydrolysed product (known as invert sugar) is laevorotatory, making the second part of Statement–I also correct.
Step 3: Examine Statement–II.
Statement–II states:
\[
\text{Laevorotation of glucose}>\text{Dextrorotation of fructose}
\]
This statement is incorrect because:
Glucose is dextrorotatory, not laevorotatory
Fructose is laevorotatory, not dextrorotatory
The magnitude of optical rotation of fructose (\(\sim 92^\circ\)) is greater than that of glucose (\(\sim 52^\circ\))
Therefore, Statement–II is false.
Step 4: Final conclusion.
Statement–I is correct
Statement–II is incorrect
Hence, the correct answer is Option (3).