A laser beam is incident at an angle of 29.8° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.62° 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.

(a) 1.5

(b)

Explanation:

Angle of incidence, = 29.8°

Angle of refraction, = 18.62°

(a) Index of refraction is given as:

The refractive index of the syrup is 1.5.

(b) Wavelength of the red light in a vacuum, λ(1)  =

Refractive index is also a ratio of the speed of the light in a vacuum with the speed of light in a particular medium:

The speed of light in a vacuum is given as;

c = λ(1) * f

=> f = c/λ(1)

The speed of light in a medium is given as;

v = λ(2) * f

=> f = v/λ(2)

(λ = wavelength and f = frequency)

We know that the frequency of light does not change when it changes media, hence, we can equate both frequencies:

c/λ(1) = v/λ(2)

Therefore:

c / v = λ(1) / λ(2)

Therefore, refractive index will become:

n = λ(1) / λ(2)

=> 1.5 =   / λ(2)

The wavelength of the red light in the solution is therefore:

λ(2) = / 1.5

λ(2) =

The wavelength of the light in the solution is

1= 26.17

2= 1.17

3=30.86

4=5.86

just took the assigment on edge

energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this