Dioptre is a unit of measurement used to quantify the optical power of a lens or the refractive error of the eye. It is defined as the reciprocal of the focal length of a lens in meters. The SI unit for dioptre is meters^-1.

Centimeter-Gram-Second (CGS) System:
The CGS system is an alternative metric system that uses centimeters, grams, and seconds as its base units. In this system, the unit of length is centimeter (cm), the unit of mass is gram (g), and the unit of time is second (s).

Conversion:
To find the CGS unit of focal length, we need to convert meters to centimeters as per the CGS system. Since 1 meter is equal to 100 centimeters, the conversion factor is 100 cm/m.

Hence, the CGS unit of focal length is centimeters^-1.

Explanation:
The focal length of a lens is the distance between the lens and the point where parallel rays of light converge or diverge. It is a crucial parameter in optics and is used to determine the magnification and image formation of a lens.

In the SI system, the focal length is measured in meters^-1. However, the CGS system uses centimeters as the base unit for length. Therefore, to convert the SI unit of focal length (meters^-1) to the CGS unit, we need to express the length in centimeters.

By multiplying the focal length in meters by the conversion factor of 100 cm/m, we obtain the focal length in centimeters^-1.

Example:
If the focal length of a lens is 0.5 dioptre, we can convert it to the CGS unit as follows:

Focal length in meters = 0.5 m
Focal length in centimeters = 0.5 m * 100 cm/m = 50 cm^-1

Therefore, the CGS unit of focal length is 50 cm^-1.

Summary:
The CGS unit of focal length is centimeters^-1. It is obtained by converting the SI unit of focal length (meters^-1) to centimeters^-1 using a conversion factor of 100 cm/m. The CGS system uses centimeters, grams, and seconds as its base units, providing an alternative metric system for various scientific measurements.