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

Step-by-step solution

We know the specific rotation, S= l C = v l m where = rotation produced I= length of the tube m= mass of sugar dissolved V= volume of sugar solution = S 1 m V For first case, = S / m V ...(i) For second case, ₁= S I₁ m₁ V₁ ...(ii) Here, I=0.2 ~m and l₁=0.3 ~m also, V₁=V+ V 2 =1.5 V= 3 2 V On dividing Eq. (ii) by Eq. (i), we get aligned ₁ =& S l₁ m V₁ S I m V = l₁ l V V₁ = l₁ l 2 V 3 V = 0.3 0.2 2 3 =1 ₁ &= aligned