Simple or rotational axis of symmetry plane of symmetry and inversion of cane sugar

What is elements of symmetry ?

In stereo-chemistry, the elements of symmetry can be defined as a specific

operations that generate the repetition of the geometric shapes of molecules which observed carrying out symmetry operation.

What is simple or rotational axis of symmetry ? 

Simple axis or rotational axis of a molecule is an imaginary axis passing through the molecule such that if the molecule rotate about 

the axis through angle of 2π/n , then the results in an orientation ,that is, super imposable on the original.It is denoted by Cn.

The higher the value of n, the axis is called principle axis.

For example, water molecule. Water molecule angular in shape and it has C2 rotational axis .

 Rotation of 180 degree about the axis will give an 

indistinguishable orientation of water molecule but the position of Ha and Hb are changed mutually.

What is plane of symmetry ?

A plane of symmetry is an imaginary plane which cuts the molecules into two parts, so that each part is the mirror image of the other. 

The molecule with such a plane are always inactive due to internal compensation.

For example, meso-tartaric acid has two asymmetric carbon atom, yet it is optically inactive because it has a plane of symmetry.

What is inversion of cane sugar or sucrose ?

On hydrolysis with dilute HCl, sucrose yield an equimolecular mixture of D(+) glucose and D(-) fructose. 

Since  D(-) fructose has a greater specific rotation than D(+) glucose, the resulting mixture is laevo rotatory. 

Because of this, the hydrolysis of cane sugar is known as the inversion of cane sugar, and the mixture is known as invert sugar.

Summary : 



What is elements of symmetry ? 
What is simple or rotational axis of symmetry ?
What is plane of symmetry ? 
What is inversion of cane sugar ? 

 Centre of symmetry and alternating axis of symmetry