As shown in figure, a ray of light is incident on glass cube. If it experiences total internal reflection in vertical plane, then what is the refractive index of glass?

Options

A. `sqrt(3/2)`
B. `((sqrt3+1))/(2)`
C. `((sqrt2+1))/(2)`
D. `(sqrt5)/(2)`

Answer

A, B, C

Explanation

At point A,`""_amu_g=(sin45^@)/(sin r)`
`therefore" "sinr=(1)/(sqrt2a^(mu)g)`
For point B,sin(`90^@`-r)=`""_gmu_a`
where, (`90^@-r)` becomes critical angle
`therefore cos r=""_gmu_g=(1)/(cosr)`
`therefore =(1)/(1-sin^2r)`
`=(1)/(sqrt(1-(1)/(2_amu_g^2)))`

`therefore ""_amu_g^2=(1)/(1-(1)/(2_amu_g^2))=(2_amu_g^2)/(2_amu_g^2-1)`
`therefore 2_amu_g^2-1=2`
`therefore ""_amu_g=sqrt(3/2)`