Light passes successively through two polarimeters tubes each of length `0.29m`. The first tube contains dextro rotatory solution of concentration `60kgm^-3` and specific rotation `0.01 rad m^2kg^-1`. The second tube contains laevo rotatory solution of concentration `30kg//m^3` and specific rotation `0.02 rad m^2kg^-1`. The net rotation produced is

Options

A. `0^(@)`
B. `15^(@)`
C. `10^(@)`
D. `20^(@)`

Answer

A

Explanation

Observed rotation for the dextrorotatory solution, `alpha=[alpha]_(D)lC`, where
`[alpha]_(D)=`specific rotation=0.01 rad `m^(2)kg^(-1)`
C=concentration=60 `kgm^(-3)`
l=length of the polarimeter tube=0.29m.
`thereforealpha_(1)=0.01xx0.29xx60=0.174` rad.
Similarly, observed rotation for laevo rotatory solution, `alpha=-[alpha]_(L)lC`
Here, `[alpha]_(L)=`specific rotation=0.02 rad `m^(2)kg^(-1)`
C=30kg `m^(-3),l=0.29m`.
`thereforealpha_(2)=0.02xx0.29xx30=-0.174rad`.
The rotations for dextrorotatory and laevo rotatory are in opposite directions. therefore, observed rotations for the two solutions are of opposite sign.
`therefore`Net rotation`=alpha_(1)+alpha_(2)=0.174-0.174`
`=0^(@)=0^(@)`