Question

In a polarimeter experiment $\theta$ is the angle of rotation produced by a given sugar solution filling the tube. Now the solution is transferred to another tube of twice the length, same diameter, remaining volume is filled with distilled water. Angle of rotation is

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

Answer 1

Answer: (C)

$\theta=s l_{1} c_{r}$
$C=$ concentration of soln.
$l=$ length of tube
$S=$ Specific rotation.
$\theta^{'}=S l_{2} C_{2}$
$c_{1}=\frac{x}{\pi r^{2} l_{1}} $
$c_{1} \propto\frac{1}{l_{1}} $
$c_{2} \propto \frac{1}{l_{2}}$
$\frac{\theta^{'}}{\theta}=\frac{S l_{2} C_{2}}{S l_{1} C_{1}}=\frac{l_{2}}{l_{1}} \times \frac{l_{1}}{l_{2}}$
$\frac{\theta^{'}}{\theta}=1 $
$\Rightarrow \theta^{'}=\theta$