Question

A cylindrical tube of length $0.2m$ and radius $R$ with sugar solution of concentration 'C' produce a rotation of $\theta$ in the plane of vibration of a plane polarized light. The same sugar solution is transferred to another tube of length $0.3m$ of same radius. The remaining gap is filled by distilled water. Now the optical rotation produced is.

• A. $\theta$
• B. $2\frac{\theta }{3}$
• C. $3\frac{\theta }{2}$
• D. $9\frac{\theta }{4}$

Answer 1

Answer: (A)

$\theta$

In first case, $\theta =S{l}_1{C}_1$
In second case, $\theta {}^{\prime }=S{l}_2{C}_2$
$l_1=0.2m$ and $l_2=0.3m$
The solution in the first tube is passed to another tube of $0m$ length, so if volume of the first tube is $v_1$ and second tube is $v_2$ and if radius of both tubes are $r$, then
$v_2=0.3\times \pi r^2=(0.2+0.1)\times \pi r^2=\frac{3v_1}{2}$
Using proportional sets to calculate concentrations of solution.
$C_1{v}_1=C_2{v}_2$
$C_2=\frac{2C_1}{3}$
Hence, $\theta {}^{\prime }=S{l}_2{C}_2=S\times 0.3\times \frac{2C_1}{3}=S\times 0.2\times C_1=\theta$