91影视

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.

The light is incident at an angle of the value $a$. It undergoes refraction inside the prism. Then assuming the angle of refraction inside the prism be $尾$and $纬$.

So, we obtain:

$$\begin{gathered} ({90}^{掳}鈥�尾)+({90}^{掳}鈥�纬)+{60}^{掳}={180}^{掳} \\ {180}^{掳}鈥�尾鈥�纬+{60}^{掳}={180}^{掳} \\ 纬={60}^{掳}鈥�尾 \end{gathered}$$

For the red light, we have: .$n_2=1.512$

For the violet light, we have: $n_2=1.530$.

Using the Snell鈥檚 law, we obtain:

$$\begin{gathered} n_1\sin \left(伪\right)=n_2\sin \left(尾\right) \\ 尾={\sin }^{鈥�1}\left(\frac{n,\sin \left(伪\right)}{n_2}\right) \\ 尾={\sin }^{鈥�1}\left(\frac{1脳\sin \left({45}^{掳}\right)}{1.512}\right) \\ 尾={\sin }^{鈥�1}\left(0.4677\right) \\ 尾=27.883 \end{gathered}$$

With the help of the above equation, we have:

$$\begin{gathered} 纬={60}^{掳}-尾 \\ 纬=60-{270883}^{掳} \\ 纬=32.{117}^{掳} \end{gathered}$$

Applying the Snell鈥檚 law and we obtain:

$$\begin{gathered} n_2\sin \left(纬\right)=n_1\sin \left({胃}_R\right) \\ {胃}_R={\sin }^{鈥�1}\left(n_2\sin \left(纬\right)\right) \\ {胃}_R={\sin }^{鈥�1}\left(1.512脳\sin \left(32.{117}^{掳}\right)\right) \\ {胃}_R=53.5^{掳} \end{gathered}$$

Therefore, the angle at which red light emerges from the prism is:$Q_R=53.5^{鈭�}$

Using the Snell鈥檚 law, we obtain:

$$\begin{gathered} n_1\sin \left(伪\right)=n_2\sin \left(尾\right) \\ 尾={\sin }^{鈥�1}\left(\frac{n_1\sin \left(伪\right)}{n_2}\right) \\ 尾={\sin }^{鈥�1}\left(\frac{1脳\sin \left({45}^{掳}\right)}{1.530}\right) \\ 尾=27.527 \end{gathered}$$

With the help of the above equation, we have:

$$\begin{gathered} 纬={60}^{鈭�}-尾 \\ 纬={60}^{鈭�}-27.{527}^{掳} \\ 纬=32.473 \end{gathered}$$

Applying the Snell鈥檚 law and we obtain:

$$\begin{gathered} \left(n_2\right)\sin \left(纬\right)=n_1\sin \left({胃}_v\right) \\ {胃}_v={\sin }^{鈥�1}\left((n_2\right)\sin \left(纬\right)) \\ {胃}_v={\sin }^{鈥�1}\left(1.53脳\sin \left(32.{473}^{鈭�}\right)\right) \\ {胃}_v=55.2^{鈭�} \end{gathered}$$

Therefore, the angle at which violet light emerges from the prism is: $Q_V=55.2^{鈭�}$.