A capillary tube is made of glass of refractive index `n'`. The outer radius of the tube is `R`. The tube is filled with a liquid of refractive index `n lt n'`. What should be the minimum internal radius of the tube so that any ray that hits the tube would enter the liquid.

Options

A. `(R )/(n)`
B. `(R )/(n')`
C. `(Rn')/(n)`
D. `(Rn)/(n')`

Explanation

The diagram shows limiting case for penetration into the liquid.
Snell's law at `S_(1)`
`rArrsinphi=(1)/(n')`….(`i`)
Snell's law for `S_(2)`
`rArrsintheta=(n)/(n')`…..(`ii`)
`sin` rule in triangle `S_(1)S_(2)O`
`rArr (sinphi)/(r )=(sin (pi-theta))/(R )`.....(`i`)
Solving the above equations we get
`r=(R )/(n)`