Question

A laser beam is incident at an angle of 30.2° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.50° to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution. nm (c) Find its frequency in the solution. Hz (d) Find its speed in the solution. m/s

Answer 1

Step-by-step explanation:

a ) Refractive index (μ ) = Sin i / Sin r

i is angle of incidence = 30.2 and r is angle of refraction = 18.5 degree

μ = Sin 30.2 / sin 18.5 = 0.5030 / .3173 = 1.585.

b ) Wave length in a medium = wavelength in air / refractive index

= 632.8 / 1.585 = 399.24 nm.

c ) frequency in solution = frequency in vacuum

=
`(3 *10^8)/(632.8* 10^(-9))`

= 47 x 10¹³ Hz

d ) Speed in the solution = Speed in vacuum / Refractive index

=
`(3* 10^8)/(1.585)`

= 1.893 x 10⁸ ms⁻¹.