Question

A TEM wave impinges obliquely on a dielectric-dielectric boundary with \(\epsilon_{r1}=2\) and \(\epsilon_{r2}=1\). The angle of incidence for total reflection is :

• A. \(30^\circ\)
• B. \(60^\circ\)
• C. \(45^\circ\)
• D. \(90^\circ\)

Hint:

For dielectric media: \[ \sin\theta_c=\sqrt{\frac{\epsilon_{r2}}{\epsilon_{r1}}} \] Total internal reflection occurs only when: \[ \epsilon_{r1}>\epsilon_{r2} \]

Answer 1

The Correct Option is C

Concept: Total internal reflection occurs when:
• Wave travels from denser medium to rarer medium.
• Angle of incidence exceeds critical angle. Critical angle is given by: \[ \sin\theta_c=\sqrt{\frac{\epsilon_{r2}}{\epsilon_{r1}}} \] for non-magnetic dielectric media.

Step 1: Identify dielectric constants. Given: \[ \epsilon_{r1}=2 \] \[ \epsilon_{r2}=1 \] Since: \[ \epsilon_{r1}>\epsilon_{r2} \] wave travels from optically denser medium to rarer medium. Hence total internal reflection is possible.

Step 2: Apply critical angle formula. Using: \[ \sin\theta_c=\sqrt{\frac{\epsilon_{r2}}{\epsilon_{r1}}} \] Substituting: \[ \sin\theta_c=\sqrt{\frac{1}{2}} \] \[ \sin\theta_c=\frac{1}{\sqrt{2}} \]

Step 3: Calculate the angle. We know: \[ \sin45^\circ=\frac{1}{\sqrt{2}} \] Therefore: \[ \theta_c=45^\circ \]

Step 4: Write the final answer. Hence, the angle for total reflection is: \[ \boxed{45^\circ} \] Therefore, the correct option is: \[ \boxed{(C)\ 45^\circ} \]