why is refractive index a dimensionless and unitless physical quantity?

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Solution

$S i n c e, r e f r a c t i v e i n d e x i s t h e r a t i o o f l i g h t o f s p e e d i n v a c u u m t o t h e s p e e d o f l i g h t i n a m e d i u m . i . e, μ = \frac{c}{v} S i n c e, n u m e r a t o r a n d d e n o m i n a t o r b o t h a r e a r e s a m e p h y s i c a l q u a n t i t i e s . H e n c e, r e f r a c t i v e i n d e x i s a u n i t l e s s a n d d i m e n s i o n l e s s q u a n t i t y w i t h d i m e n s i o n s [M^{0} L^{0} T^{0}]$

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