Question

If the critical angle in a medium is \( \alpha \), then for total internal reflection the angle of incidence \( \beta \) should be:

• A. \( \beta < \alpha \)
• B. \( \beta > \alpha \)
• C. \( \beta = \alpha \)
• D. \( \beta \leq \alpha \)

Hint:

Total internal reflection happens only when the ray goes from denser to rarer medium and the angle of incidence exceeds the critical angle.

Answer 1

The Correct Option is B

Step 1: Recall the condition for total internal reflection (TIR).
Total internal reflection can occur only when light travels from an optically denser medium to an optically rarer medium (for example, glass to air).

Step 2: Meaning of the critical angle.
The critical angle \( \alpha \) is that particular angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes exactly \( 90^\circ \). At this angle the refracted ray just grazes along the boundary surface.

Step 3: What happens for different angles of incidence.
Using Snell's law at the boundary, \( n \sin\beta = \sin r \), where \( r \) is the angle of refraction.
• If \( \beta < \alpha \): the ray refracts and passes into the rarer medium (\( r < 90^\circ \)).
• If \( \beta = \alpha \): the refracted ray grazes the surface (\( r = 90^\circ \)).
• If \( \beta > \alpha \): refraction is impossible, so the whole light is reflected back into the denser medium. This is total internal reflection.

Step 4: Choose the correct option.
TIR requires the angle of incidence to be greater than the critical angle. Therefore \( \beta > \alpha \), which is option (ii).
Options (i), (iii) and (iv) all allow \( \beta \) to be equal to or less than \( \alpha \), for which the light still refracts out and no total internal reflection occurs.

\[\boxed{\beta > \alpha}\]