Step 1: Concept Definition:
The critical angle is the angle of incidence at which light, traveling from a denser to a rarer medium, refracts at an angle of 90°. This is the condition for total internal reflection.
Step 2: Governing Law:
Snell's Law states:
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]
Here, \(n_1\) and \(n_2\) are the refractive indices of the denser and rarer media, respectively. \(\theta_1\) is the angle of incidence, and \(\theta_2\) is the angle of refraction. The critical angle (\(i_c\)) is the angle of incidence (\(\theta_1\)) when the angle of refraction (\(\theta_2\)) is 90°. At this angle, the refracted ray travels along the interface between the two media.
Step 3: Derivation and Implications:
When light moves from a denser medium (\(n_1\)) to a rarer medium (\(n_2\)) (i.e., \(n_1>n_2\)), increasing the angle of incidence (\(\theta_1\)) also increases the angle of refraction (\(\theta_2\)).A specific angle of incidence, the critical angle \(i_c\), results in an angle of refraction of 90°.Substituting \(\theta_1 = i_c\) and \(\theta_2 = 90^\circ\) into Snell's Law:
\[ n_1 \sin i_c = n_2 \sin 90^\circ \]
Since \(\sin 90^\circ = 1\):
\[ \sin i_c = \frac{n_2}{n_1} \]
If the angle of incidence exceeds the critical angle (\(\theta_1>i_c\)), light does not refract but is entirely reflected back into the denser medium. This is known as total internal reflection.Therefore, the critical angle is precisely the angle of incidence that yields a 90° angle of refraction. Other angles are incorrect: the angle of reflection equals the angle of incidence, meaning it would be \(i_c\), not 0° or 90°. An angle of refraction of 0° occurs at normal incidence (\(\theta_1=0^\circ\)).
Step 4: Conclusion:
The critical angle is defined as the angle of incidence for which the angle of refraction is 90°.