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 18.82° 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.

Answer 1

a) n2 = 1.55

b) 408.25 nm

c) 4.74*10^14 Hz

d) 1.93*10^8 m/s

Step-by-step explanation:

a) To find the index of refraction of the syrup solution you use the Snell's law:

`n_1sin\theta_1=n_2sin\theta_2` (1)

n1: index of refraction of air

n2: index of syrup solution

angle1: incidence angle

angle2: refraction angle

You replace the values of the parameter in (1) and calculate n2:

`n_2=(n_1sin\theta_1)/(sin\theta_2)=((1)(sin30.2\°))/(sin18.82\°)=1.55`

b) To fond the wavelength in the solution you use:

`(\lambda_2)/(\lambda_1)=(n_1)/(n_2)\\\\\lambda_2=\lambda_1(n_1)/(n_2)=(632.8nm)(1.00)/(1.55)=408.25nm`

c) The frequency of the wave in the solution is:

`v=\lambda_2 f_2\\\\f_2=(v)/(\lambda_2)=(c)/(n_2\lambda_2)=(3*10^8m/s)/((1.55)(408.25*10^(-9)m))=4.74*10^(14)\ Hz`

d) The speed in the solution is given by:

`v=(c)/(n_2)=(3*10^8m/s)/(1.55)=1.93*10^8m/s`