Question

The critical angle of incidence \(i_c\) for a ray incident from a denser to rarer medium, is that angle for which

• A. the angle of reflection is 90°
• B. the angle of refraction is 90°
• C. the angle of refraction is 0°
• D. the angle of reflection is 0°

Hint:

Remember the two conditions for total internal reflection (TIR): 1. Light must travel from a denser medium to a rarer medium. 2. The angle of incidence in the denser medium must be greater than the critical angle. The critical angle itself is the "tipping point" where the refracted ray just skims the surface.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The critical angle is a specific angle of incidence that occurs only when light travels from a denser medium to a rarer medium. It is the boundary condition for the phenomenon of total internal reflection.

Step 2: Key Formula or Approach:
According to Snell's Law of refraction: \[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \] where \(n_1\) and \(n_2\) are the refractive indices of the first (denser) and second (rarer) media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction, respectively. The critical angle (\(i_c\)) is the angle of incidence (\(\theta_1\)) for which the angle of refraction (\(\theta_2\)) is exactly 90°. At this point, the refracted ray grazes the boundary between the two media.

Step 3: Detailed Explanation:
When light travels from a denser medium (\(n_1\)) to a rarer medium (\(n_2\)), where \(n_1 > n_2\), as the angle of incidence \(\theta_1\) increases, the angle of refraction \(\theta_2\) also increases. There exists a particular angle of incidence, called the critical angle \(i_c\), for which the angle of refraction becomes 90°. Setting \(\theta_1 = i_c\) and \(\theta_2 = 90^\circ\) in Snell's Law: \[ n_1 \sin i_c = n_2 \sin 90^\circ \] Since \(\sin 90^\circ = 1\), we get: \[ \sin i_c = \frac{n_2}{n_1} \] If the angle of incidence is greater than the critical angle (\(\theta_1 > i_c\)), the light ray does not refract into the rarer medium at all; instead, it is completely reflected back into the denser medium. This phenomenon is called total internal reflection. Therefore, the critical angle is defined as the angle of incidence that results in an angle of refraction of 90°. The other options are incorrect: the angle of reflection is always equal to the angle of incidence, so it would be \(i_c\), not 0° or 90°. An angle of refraction of 0° corresponds to normal incidence (\(\theta_1=0^\circ\)).

Step 4: Final Answer:
The critical angle is the angle of incidence for which the angle of refraction is 90°.