How do the spacings of the three planes ( 100), ( 101) and ( 111) of simple cubic lattice vary ?

Explanation

Simple Cubic Lattice
100,101,111

`d_(hkl)= ( a)/( sqrt(h^(2) + k^(2) + l^(2)))`
`= d_(100) = ( 1)/(sqrt(1^(2) + 0^(2) + 0^(2)))=1`
`= d_(101) = ( 1)/( sqrt(1^(2) + 0^(2) + 0^(2))) = (1)/( sqrt(2))`
`d_(111) = ( 1)/( sqrt(1^(2) + 1^(2) + 1^(1))) = ( 1)/( sqrt(3))`
` d_(100) : d_(101) : d_(111) = 1: ( 1)/( sqrt(2)) : ( 1) /( sqrt(3))` ( or )
`= 1: 0.707: 0.577`