Question

(a) Name the electromagnetic radiation used to detect fake currency.
(b) Redraw the diagram given below and complete the path of the light ray AB through the glass prism till it emerges out of the prism. Critical angle of the glass is 42\(^\circ\).

Hint:

When a ray hits a boundary, always find the angle of incidence and compare it to the critical angle. If \(i>c\), TIR occurs. If \(i<c\), refraction occurs. If \(i = c\), the ray grazes the surface.

Answer 1

(a) Electromagnetic Radiation:
Ultraviolet (UV) radiation is used to detect fake currency. Genuine banknotes often have fluorescent security features that are invisible in normal light but glow under UV light.
(b) Path of the light ray:

Explanation of the path: 1. Entry at the first surface: The light ray AB strikes the vertical face of the prism normally (at 90\(^\circ\)). Therefore, its angle of incidence is 0\(^\circ\), and it passes into the prism without any deviation.
2. Incidence at the hypotenuse: The ray travels horizontally inside the prism and strikes the hypotenuse. The angles of the prism are 90\(^\circ\), 30\(^\circ\), and 60\(^\circ\). The angle of incidence (\(i\)) at the hypotenuse is 60\(^\circ\).
3. Check for Total Internal Reflection (TIR): The critical angle (\(c\)) for the glass is given as 42\(^\circ\). Since the angle of incidence (\(i = 60^\circ\)) is greater than the critical angle (\(c = 42^\circ\)), the ray undergoes Total Internal Reflection.
4. Reflection: The ray reflects from the hypotenuse following the laws of reflection, so the angle of reflection is also 60\(^\circ\).
5. Emergence from the base: The reflected ray travels downwards and strikes the horizontal base of the prism at 90\(^\circ\) (normally). Therefore, it emerges from the prism without any deviation.