Question

Light with a wavelength of 589 nm in a vacuum strikes the surface of an unknown liquid at an angle of 31.2° with respect to the normal to the surface. If the light travels at a speed of 1.97 × 10⁸ m/s through the liquid, what is the angle of refraction?

Answer 1

wavelength = 589 x 10 -9 m

Angle of incidence i = 31.2 ^o

Speed of light v = 1.97 x 10 ⁸ m/ s

Angle of refraction r = ?

Index of refraction of the liquid n = c / v

Where c = speed of light in vacuum

              = 3 x 10 ⁸ m / s

Substitute values you get n = 1.5228

From snell's law    n = sin i / sin r

From this   sin r = sin i / n

                        = (sin 31.2 ) / 1.5228

                        = 0.34

From this r = sin ^-1 ( 0.34 )

                  = 19.88 ^o