Monochromatic light falls at an angle of incidence i on a slab of a transparent material (refractive index `mu`). If reflected and refracted rays are mutually perpendicular, find the relation between `mu` and `i`.

Explanation

In the given figure let r is the angle of reflection and r . is the angle of refraction. According to the given condition, considering the reflected and the refracted rays to be perpendicular to each other
`:. ` From the figure r +`90^(@)` + r. =`180^(@)`
So,` r. =90^(@)`-r
`r. =90^(@)-i `[i-r , by law of reflaction]
acc to snell.s law ,I sini = `mu`sinr.
sini = `mu`sin(`90^(@)`-i)
sini = `mu`cosi , `mu` = tan i `implies` i = `tan^(-1)(mu)`