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

Answer:

1.29649

488.08706 nm

$6.14644\times 10^{14}\ Hz$

231715700.28346 m/s

Explanation:

n denotes refractive index

1 denotes air

2 denotes solution

$\lambda_0$ = 632.8 nm

From Snell's law we have the relation

$n_1sin\theta_1=n_2sin\theta_2\\\Rightarrow n_2=\dfrac{n_1sin\theta_1}{sin\theta_2}\\\Rightarrow n_2=\dfrac{1\times sin33}{sin24.84}\\\Rightarrow n_2=1.29649$

Refractive index of the solution is 1.29649

Wavelength is given by

$\lambda=\dfrac{\lambda_0}{n_2}\\\Rightarrow \lambda=\dfrac{632.8}{1.29649}\\\Rightarrow \lambda=488.08706\ nm$

The wavelength of the solution is 488.08706 nm

Frequency is given by

$f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^8}{488.08706\times 10^{-9}}\\\Rightarrow f=6.14644\times 10^{14}\ Hz$

The frequency is $6.14644\times 10^{14}\ Hz$

$v=\dfrac{c}{n_2}\\\Rightarrow v=\dfrac{3\times 10^8}{1.29469}\\\Rightarrow v=231715700.28346\ m/s$

The speed in the solution is 231715700.28346 m/s