Light is incident normally on the face AB of a prism as shown in figure. A liquid of refractive index n is placed on face AC of the prism. The prism is made of glass of refractive index `sqrt3`. The limiton n for which total internal reflection takes place on face AC is ...........

Options

A. `n gt sqrt3`
B. `n lt 3/2`
C. `n=sqrt3`
D. `n gt 3/2`

Answer

B, C

Explanation

Refractive index of prism relative to liquid is
`n_p=("nprism")/("nliquid")=(sqrt3)/(n)` …(1)
`sin c=(1)/(""^ln_p)=(n)/(sqrt3)` …(3)
For total internal reflection i `gt` c
sin i `gt` sin c
`therefore sin 60 gt (n)/(sqrt3)`
`therefore(sqrt3)/(2)=(n)/(sqrt3)" "therefore n lt 3/2`