A ray of light normally on one of the faces of a right-angled isosceles glass prism is found to be totally reflected. What is the minimum value of the refractive index of the material of the prism ?

Options

A. `sqrt(2)`
B. `sqrt((3)/(2))`
C. `4//3`
D. `3//4`

Answer

A

Explanation

For total internal reflaction to take place AB
`igtC` or `sinigtsinC`
where, `i=`Angle of incidence
C=Critical angle
Here, `i=45^(@)` and `sinC=(1)/(mu)`
`:.sin45^(@)gt(1)/(mu)implies(1)/(sqrt(2))gt(1)/(mu)` or `mugtsqrt(2)`
`:.mu_("min")=sqrt(2)`