Question

Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of $\mathbf{45}\mathbf{.}{\mathbf{0}}^{\mathbf{°}}$, and you observe the angle of refraction to be$\mathbf{40}\mathbf{.}{\mathbf{3}}^{\mathbf{°}}$. What is the index of refraction of the substance and its likely identity?

Short answer

The value ofn=1.46 which depicts the unknown material mostly to be the fused quartz.

Step-by-step solution

Define Geometric Optics

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.

Evaluating the index of refraction and its identity

Using the Snell's law:

$(n_i\sin {\theta }_i=n_f\sin {\theta }_f)$

It is used to identify the coefficient of refraction of the unknown substance, and then we use the table 25.1 to select the most effective substance among the mentioned materials.

$$\begin{gathered} n_f=\frac{n_i\sin {\theta }_i}{\sin {\theta }_f} \\ =\frac{1.33\times \sin .45.0°}{\sin 40.3°} \\ =1.46 \end{gathered}$$

With the help of the table 25.1, the unknown material is most probably the fused quartz.

Therefore, the value of n=1.46 which is the unknown material, mostly fused quartz.