The graph between sine of angle of refraction (sin r) in medium 2 and sine of angle of incidence (sin i) in medium 1 indicates that (tan 36 degrees = 3/4). A. Total internal reflection can take place B. Total internal reflection cannot take place C. Any of a and b D. Data is incomplete
Question
The graph between sine of angle of refraction $(\sin r)$ in medium 2 and sine of angle of incidence $(\sin i)$ in medium 1 indicates that $\left(\tan 36^{\circ}=\frac{3}{4}\right)$.
A. Total internal reflection can take place
B. Total internal reflection cannot take place
C. Any of a and b
D. Data is incomplete
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Answer
Given the problem, we are provided with a graph depicting the relationship between $\sin r$ (sine of the angle of refraction in medium 2) and $\sin i$ (sine of the angle of incidence in medium 1). The problem also specifies that $\tan 36^{\circ} = \frac{3}{4}$.
We need to determine if total internal reflection can take place by analyzing the provided graph.
:

Graph Analysis:
The graph shows the relationship between $\sin r$ and $\sin i$. From the graph, we can deduce the slope which is given by the angle $\frac{2\pi}{10} = 36^{\circ}$. 
Calculating the Refractive Index:
Using the slope of the line: $$ \tan 36^{\circ} = \frac{\sin i}{\sin r} $$ Given $\tan 36^{\circ} = \frac{3}{4}$, we find: $$ \frac{\sin i}{\sin r} = \frac{3}{4} $$ 
Applying Snell's Law:
According to Snell's Law: $$ \frac{\sin i}{\sin r} = \frac{n_2}{n_1} $$ where $n_2$ and $n_1$ are the refractive indices of medium 2 and medium 1, respectively.From the given ratio, we equate: $$ \frac{n_2}{n_1} = \frac{3}{4} $$
This means: $$ n_2 = \frac{3}{4} n_1 $$

Relative Refractive Indices:
Given that $n_2 < n_1$, medium 2 is less optically dense than medium 1. 
Understanding Total Internal Reflection (TIR):
Total internal reflection occurs only when light travels from a denser to a rarer medium. Here, since medium 2 is less dense than medium 1, total internal reflection is not possible.
Conclusion:
Total internal reflection cannot take place. Therefore, the correct answer is:
B. Total internal reflection cannot take place.
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