Question

Figure shows graph of angle of deviation v/s angle of incidence for a light ray. Incident ray goes from medium 1($\mu_1$) to medium 2($\mu_2$).

• A. $\theta_1$ = 90°
• B. Critical angle 45°
• C. $\mu_1 < \mu_2$
• D. $\theta_2$ = 60
• E. $\theta_3$ = 90

Answer 1

Answer: (A), (B), (E)

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Answer 2

The problem presents a graph of the angle of deviation ($\delta$) versus the angle of incidence ($i$) for a light ray traveling from medium 1 ($\mu_1$) to medium 2 ($\mu_2$). We need to evaluate the correctness of five statements based on this graph.

Analysis of the graph:

1. Region 1 (Refraction): The graph shows a curved path from $i=0^\circ$ to $i=45^\circ$. This corresponds to refraction. At $i=0^\circ$ (normal incidence), $\delta=0^\circ$, which is expected.
2. Region 2 (Total Internal Reflection - TIR): At $i=45^\circ$, the nature of the graph changes abruptly, and for $i > 45^\circ$, it becomes a straight line with a negative slope. This change indicates that $i=45^\circ$ is the critical angle ($i_c$), and for angles of incidence greater than $i_c$, Total Internal Reflection (TIR) occurs. The straight line represents deviation during TIR.

(b) Critical angle 45°: As observed from the graph, the transition from refraction to TIR occurs at $i=45^\circ$. Therefore, the critical angle ($i_c$) is $45^\circ$. This statement is correct.

(c) $\mu_1 < \mu_2$: For Total Internal Reflection (TIR) to occur, light must travel from a denser medium to a rarer medium. Since TIR is observed in the graph, it implies that medium 1 is denser than medium 2, i.e., $\mu_1 > \mu_2$. From the critical angle, $\sin i_c = \frac{\mu_2}{\mu_1}$. $\sin 45^\circ = \frac{1}{\sqrt{2}}$. So, $\frac{\mu_2}{\mu_1} = \frac{1}{\sqrt{2}}$, which means $\mu_1 = \sqrt{2}\mu_2$. This confirms $\mu_1 > \mu_2$. This statement is incorrect.

(a) $\theta_1 = 90^\circ$: The graph for TIR extends up to $\theta_1$. The maximum possible angle of incidence is $90^\circ$ (grazing incidence). At this angle, the ray is incident parallel to the interface. For TIR, this ray would also undergo reflection. Thus, $\theta_1$ represents the maximum possible angle of incidence, which is $90^\circ$. This statement is correct.

(d) $\theta_2 = 60$: $\theta_2$ is the angle of deviation at the critical angle ($i_c = 45^\circ$). When light goes from a denser medium ($\mu_1$) to a rarer medium ($\mu_2$), it bends away from the normal, so the angle of refraction ($r$) is greater than the angle of incidence ($i$). The deviation is $\delta = r - i$. At the critical angle, $i = i_c = 45^\circ$, and the angle of refraction $r = 90^\circ$. Therefore, $\theta_2 = \delta(i_c) = r - i_c = 90^\circ - 45^\circ = 45^\circ$. Since $\theta_2 = 45^\circ$, the statement $\theta_2 = 60$ is incorrect.

(e) $\theta_3 = 90$: $\theta_3$ is the angle of deviation when $i = \theta_1 = 90^\circ$.

Therefore, the correct set of statements is (a), (b), and (e).