AB and CD are surfaces of two slabs as shown in figure. The medium between the slabs has refractive index 2, refractive index of slab above `AB` is `sqrt2` and below CD is `sqrt3`. Find the minimum angle of incidence, so that the ray is totally reflected by both the slabs.

Explanation

Critical angle
`mu_2sinC=mu_1sin90^@`
`2sinC=sqrt2impliessinC=1/sqrt2=sin45^@`
`C=45^@`
For T.I.R. at AB, `igtC` i.e. `igt45^@`

Critical angle
`mu_2sinC^'=mu_3sin90^@`
`2sinC^'=sqrt3impliessinC^'=sqrt3/2=sin60^@`
`C^'=60^@`
For T.I.R. at CD, `igtC^'` i.e. `igt60^@`
`i_(min)=60^@`