A ray of light passes from glass, having a refractive index of 1.6, to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is

Options

A. `sin^(-1)((4)/(5))`
B. `sin^(-1)(3/(5))`
C. `sin^(-1)((5)/(8))`
D. `sin^(-1)((2)/(5))`

Answer

b.

Explanation

`._gmu_(a)=(sini)/(sinr)`
`(1)/(._amu_(g))=(sini)/(sin2i)`
`(1)(16)=(sini)/(2sini cosi) or (1)/(cosi)(1)/(10)=(5)/(8)`
or `(1)/(cosi)=(5)/(4)` or `cosi=(4)/(5)`
Now, `sini= sqrt(1-cos^(2))i`
or `sini=sqrt(1-(16)/(25))=sqrt((9)/(25))=(3)/(5)`
or `i=sin^(-1)((3)/(5))`