Question

A Parallel beam of monochromatic light is incident on a plane reflecting surface. If width of the plane incident and reflected plane wavefront is represented by \(AB\) and \(CD\) respectively then

• A. \(AB>CD\)
• B. \(AB\lt CD\)
• C. \(AB=CD\)
• D. \(AB>>CD\)

Hint:

By the law of reflection the angles of incidence and reflection are equal, so the wavefront keeps the same width after reflection.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A parallel beam gives a plane wavefront. When it reflects from a plane surface the reflected wavefront is also plane.

Step 2: Use the Geometry
If the beam covers a length \(L\) of the surface, then \(AB=L\cos i\) and \(CD=L\cos r\), where \(i\) and \(r\) are the angles of incidence and reflection.

Step 3: Apply the Law of Reflection
The law of reflection gives \(i=r\), so \(\cos i=\cos r\).

Step 4: Compare the options
Hence \(AB=CD\), which is option (C).

Final Answer:
The widths of the incident and reflected wavefronts are equal, \(AB=CD\). \[ \boxed{\text{(C) }AB=CD} \]