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  4. Specific rotation of sugar solution is 0.01 SI units. 200 kgm -3 of impure sugar solution is taken in a polarimeter tube of length 0.25 m and an optical rotation of 0.4 rad is observed. The percentage of purity of sugar is the sample is

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Q. Specific rotation of sugar solution is $0.01$ SI units. $200 \,kgm ^{-3}$ of impure sugar solution is taken in a polarimeter tube of length $0.25 \,m$ and an optical rotation of $0.4$ rad is observed. The percentage of purity of sugar is the sample is

Wave Optics

Solution:

Specific rotation
$(\alpha)=\frac{\theta}{l c} $
$\Rightarrow c=\frac{\theta}{\alpha l}=\frac{0.4}{0.01 \times 0.25}=160\, kg / m ^{3}$
Now percentage purity of sugar solution
$=\frac{160}{200} \times 100=80 \%$