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.

Using Snell's law: $n_i\sin {\mathrm{θ}}_i=n_f\sin {\mathrm{θ}}_f$, it is along with trigonometry that is applied in the figure below, we can find that by using $\tan {\mathrm{θ}}_1=\frac{x_2}{d}$, and $\tan {\mathrm{θ}}_2=\frac{x_1}{d}$. Besides: $∆x=x_2-x_1$.

The diagram is represented as:

The equation is then evaluated as:

$$\begin{gathered} {\mathrm{θ}}_2={\sin }^{-1}\left(\frac{n_1\sin {\mathrm{θ}}_1}{n_2}\right) \\ ={\sin }^{-1}\left(\frac{1.00×\sin 40.0^{°}}{1.52}\right) \\ =25.0^{°} \\ âˆ\mu \tan {\mathrm{θ}}_2=\frac{x_1}{d} \\ ∴x_1=d×\tan {\mathrm{θ}}_2 \\ âˆ\mu \tan {\mathrm{θ}}_1=\frac{x_2}{d} \\ ∴x_2=d×\tan {\mathrm{θ}}_1 \end{gathered}$$

$$\begin{gathered} ∆x=x_2-x_1 \\ =d×\left(\tan {\mathrm{θ}}_1-\tan {\mathrm{θ}}_2\right) \\ =0.01m×\left(\tan 40.0^{°}-\tan 25.0^{°}\right) \\ =3.73×{10}^{-3}m \\ =3.73mm \end{gathered}$$

Therefore, the amount of rays displayed by the glass is: 3.73mm.