Question

The observed rotation is dependent on the number of molecules in the path of the light. If a sample 10 cm deep has a rotation of +270°, what would be the observed rotation for a 6 cm deep sample of the same material?

Answer 1

We have

Specific rotation ([α]_λ^T) of an optically active compound is as follows:

α = observed rotation measured using a polarimeter
l = length of sample tube
C = concentration

T = Temperature (usually 25 ºC)
λ = wave length of the light used

There fore

alpha the observed rotation = specific rotation x l x c

that is

alpha = specificrot. x l x c

[alpha is directly proportional to l ]

given

alpha = + 270 when l = 10 cm

Let

Alpha = Y when l = 6 cm

So,

          + 270 = 10 -------- equation 1

          Y = 6      ------------ equation 2

From equation 1 and 2

Y = 6 x 270 / 10 = + 162

So the answer = + 162