A glass prism has a right-triangular cross section ABC, with `angleA = 90^(@)`. A ray of light parallel to the hypotenuse BC and incident on the side AB emerges grazing the side AC. Another ray, again parallel to the hypotenuse BC, incident on the side AC suffers total internal reflection at the side AB. Which one of the following must be true about the refractive index `mu` of the material of the prism ?

Options

A. `sqrt((3)/(2)) lt mu lt sqrt(2)`
B. `mu gt sqrt(3)`
C. `mu lt sqrt((3)/(2))`
D. `sqrt(2) lt mu lt sqrt(3)`

Answer

A

Explanation

`sin alpha = mu sin theta " "`…(i)
`mu cos theta = 1 " "`…. (ii)
`mu^(2) - 1 + sin^(2) alpha " "`…(iii)
`mu cos beta gt 1 " "`....(iv)
`mu^(2) gt 1 + cos^(2) alpha " " rArr 2mu^(2) gt 3 rArr mu gt sqrt((3)/(2))`
For `mu_(max) , alpha = 45^(@) " " rArr mu_(max) lt sqrt(2) `
`rArr sqrt((3)/(2)) lt mu lt sqrt(2)`