A glass block in air has a critical angle of 49°. What will happen to a ray of light coming through the glass hen it is incident at an angle of 50° at the glass-air boundary? Illustrate with a diagram.
The correct answer and explanation is :
Correct Answer:
The ray of light will undergo total internal reflection.
Explanation:
In optics, total internal reflection happens when a light ray traveling inside a denser medium (like glass) hits the boundary with a less dense medium (like air) at an angle greater than the critical angle. Instead of refracting (bending) into the less dense medium, the light reflects completely back into the denser medium.
In this situation:
- The critical angle is given as 49°.
- The light ray is incident at 50°, which is greater than the critical angle.
The critical angle is the minimum angle of incidence in the denser medium at which the light ray is refracted exactly along the boundary (making a 90° angle with the normal). When the incidence angle exceeds this critical value, no refraction occurs. Instead, the ray reflects entirely inside the glass, obeying the law of reflection (angle of incidence equals angle of reflection).
This can be better understood by Snell’s Law:
[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
]
where:
- ( n_1 ) = refractive index of glass
- ( n_2 ) = refractive index of air (approximately 1.0)
- ( \theta_1 ) = angle of incidence
- ( \theta_2 ) = angle of refraction
At the critical angle, ( \theta_2 = 90^\circ ), so:
[
n_1 \sin(\theta_c) = n_2
]
Since ( \theta_1 = 50^\circ > \theta_c = 49^\circ ), Snell’s Law cannot be satisfied with a real angle of refraction (you would get the sine of a value greater than 1, which is impossible). Hence, the light cannot refract into air and must totally reflect back into the glass.
Thus, a ray of light hitting the glass-air boundary at an angle of 50° will not exit the glass but will instead reflect entirely within the glass, following the law of reflection.