a glass slab of thickness 4cm contains the same no of wavelength 5 cm of water when both are travnersed by same monochromatic light .calculate the r.i of glass

Question

a glass slab of thickness 4cm contains the same no of wavelength
5 cm of water when both are travnersed by same monochromatic light
calculate the r i of glass

Jyoti Pant · Accepted Answer

Let wavelength in glass= $λ_{g}$ , wavelength in water= $λ_{w}$

also number of waves in 4cm glass=no.of waves in 5 cm water

$S o \frac{4}{λ_{g}} = \frac{5}{λ_{w}} o r λ_{g} = \frac{4}{5} λ_{w} \frac{υ_{g}}{ν} = \frac{4}{5} \frac{υ_{w}}{ν} (S i n c e λ = \frac{υ}{ν}) υ_{g} = \frac{4}{5} υ_{w} N o w n = \frac{c}{υ} (a b s o l u t e r e f r a c t i v e i n d e x = \frac{s p e e d o f l i g h t i n v a c u u m / a i r}{s p e e d o f l i g h t i n t h e m e d i u m}) s o n_{g} = \frac{c}{υ_{g}} a n d n_{w} = \frac{c}{υ_{w}} d i v i d i n g n_{g} b y n_{w}, w e g e t \frac{n_{g}}{n_{w}} = \frac{υ_{w}}{υ_{g}} = \frac{υ_{w}}{\frac{4}{5} υ_{w}} = \frac{5}{4} o r n_{g} = \frac{5}{4} \times \frac{4}{3} = \frac{5}{3} (\sin c e refractive index of water=4/3 )$