91Ó°ÊÓ

Geometrical optics, often known as ray optics, is an optics model that describes light propagation using rays. In geometric optics, a ray is an abstraction that can be used to approximate the routes along which light propagates under particular conditions.

To evaluate the angle of refraction for each light color using Snell's law:$n_i\sin {\mathrm{θ}}_i=n_f\sin {\mathrm{θ}}_f$.

The value of$n_f=1.000$.

The angle evaluated for yellow light is:

$$\begin{gathered} {\mathrm{θ}}_f={\sin }^{-1}\left(\frac{n_i\sin {\mathrm{θ}}_i}{n_f}\right) \\ ={\sin }^{-1}\left(\frac{1.492×\sin 30.{00}^{°}}{1.000}\right) \\ =48.{25}^{°} \end{gathered}$$

Therefore, the angle for yellow light is: $48.{25}^{°}$.

The angle evaluated for green light is:

$$\begin{gathered} {\mathrm{θ}}_f={\sin }^{-1}\left(\frac{n_i\sin {\mathrm{θ}}_i}{n_f}\right) \\ ={\sin }^{-1}\left(\frac{1.493×\sin 30.{00}^{°}}{1.000}\right) \\ =48.{29}^{°} \end{gathered}$$

Therefore, the angle for yellow light is: $48.{29}^{°}$.

The value of$∆y=1.00mm$ and then we solve for the value of $∆x$.

It is then evaluated as:

$$\begin{gathered} ∆x=\frac{∆y}{\tan {\mathrm{θ}}_f} \\ =\frac{1.00×{10}^{-3}m}{\tan 0.{04}^{°}} \\ =1.43m \end{gathered}$$

Therefore, the distance is: 1.43m.