Question

A laser beam is incident at an angle of 33.0° to the vertical onto a solution of cornsyrup in water.(a) If the beam is refracted to 24.84° to the vertical, what is the index ofrefraction of the syrup solution?(b) Suppose the light is red, with wavelength 632.8 nm in a vacuum.Find its wavelength in the solution.(c) What is its frequencyin the solution?(d) What is its speed in the solution?

Answer 1

1.29649

488.08706 nm

`6.14644* 10^(14)\ Hz`

231715700.28346 m/s

Step-by-step explanation:

n denotes refractive index

1 denotes air

2 denotes solution

`\lambda_0` = 632.8 nm

From Snell's law we have the relation

`n_1sin\theta_1=n_2sin\theta_2\\\Rightarrow n_2=(n_1sin\theta_1)/(sin\theta_2)\\\Rightarrow n_2=(1* sin33)/(sin24.84)\\\Rightarrow n_2=1.29649`

Refractive index of the solution is 1.29649

Wavelength is given by

`\lambda=(\lambda_0)/(n_2)\\\Rightarrow \lambda=(632.8)/(1.29649)\\\Rightarrow \lambda=488.08706\ nm`

The wavelength of the solution is 488.08706 nm

Frequency is given by

`f=(c)/(\lambda)\\\Rightarrow f=(3* 10^8)/(488.08706* 10^(-9))\\\Rightarrow f=6.14644* 10^(14)\ Hz`

The frequency is
`6.14644* 10^(14)\ Hz`

`v=(c)/(n_2)\\\Rightarrow v=(3* 10^8)/(1.29469)\\\Rightarrow v=231715700.28346\ m/s`

The speed in the solution is 231715700.28346 m/s