Wave Optics

Reflection of light on a plane reflecting surface follows the laws of reflection:
1. The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
2. The angle of incidence ( ) is equal to the angle of reflection ( ).
When a ray of light strikes a plane mirror, it bounces back with , maintaining the direction in the same plane.
Diagram:
\includegraphics[width=0.5\linewidth]{Reflection of light.png} The diagram shows the incident ray, normal, and reflected ray with .
Answer: Reflection follows two laws; incident and reflected rays are symmetric about the normal.

Wavelength .
Fringe width , where (screen distance), is slit separation.
Total separation of 10 bright fringes = .
Answer: 0.6 mm.

In Young's double slit experiment, for amplitudes and , intensity .
Let . Then: Answer: 5 : 3.

When light travels from one medium to another, its speed and wavelength change due to the refractive index ( , ). Frequency remains constant as it depends on the source, not the medium ( ).
Answer: frequency.

Step 1: In Young’s double-slit experiment, the distance of the -th bright fringe from the central fringe is given by: Since the setup remains unchanged, the ratio of fringe positions is: Step 2: Given cm, \bigskip

Brewster's Law: This law states that for a particular angle of incidence, known as Brewster's angle or the polarizing angle ( ), the reflected light from a transparent dielectric surface is completely plane-polarized. This occurs when the reflected ray and the refracted ray are perpendicular to each other.
Derivation:
Let unpolarized light be incident at Brewster's angle on the surface separating two media (e.g., air and glass) with refractive indices and respectively. Let be the angle of refraction.
According to Snell's law: By the condition of Brewster's law, the reflected and refracted rays are perpendicular. From the geometry of reflection and refraction, this means: Now, substitute this value of into Snell's law (equation 1): Since , the equation becomes: Rearranging the terms to find the angle : If the first medium is air or vacuum ( ) and the second medium has refractive index ( ), the formula simplifies to: This is the formula for Brewster's angle.