Which condition is necessary for total internal reflection? a. the refracted ray should lie along the boundary of the two media. b. the refracted ray should turn toward the normal. c. light in a medium is incident on a boundary with a faster medium. d. light in a medium is incident on a boundary with a slower medium.

There are two conditions necessary for total internal reflection, which is when light hits the boundary between two mediums and reflects back into its original medium:

Light is about to pass from a more optically dense medium (slower) to a less optically dense medium (faster).

The angle of incidence is greater than the defined critical angle for the two mediums, which is given by:

θ = sin⁻¹(/)

Where θ = critical angle, = refractive index of faster medium, = refractive index of slower medium.

Choice C gives one of the above necessary conditions.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west