why use 0.008856 in Lab color space?

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Yoon ThiriZaw 2019-5-26

In Lab color space equations, why use 0.008856 as thresholds if we transform RGB to Lab? Lab color space equation are the following:

•The conversion formula of RGB image into Lab image is:

X = 0.4124*R + 0.3576*G + 0.1805*B

Y = 0.2126*R + 0.7152*G + 0.8220*B

Z = 0.0193*R + 0.1192*G + 0.9505*B

If X/X_n,Y/Y_n,Z/Z_nare all greater than 0.008856,then

L* = 116∛("Y/" Y_n )- 16

a* = 500 ( ∛("X/" X_n )- ∛("Y/" Y_n ))

b* = 200 (∛("Y/" Y_n )- ∛("Z/" Z_n ))

If X/X_n,Y/Y_n,Z/Z_nare all equal to or less than 0.008856,then

L* = 903.3(Y/Y_n,)

a* = 500 (f(X/X_n,) – f(Y/Y_n))

b* = 200 (f(Y/Y_n) – f(Z/Z_n))

Why let these thresholds 0.008856?

If less than 0.008856, what we get?

And, if greater than 0.008856, what we get?

Please!!!

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