Question

A vertical narrow wire is illuminated with laser. Alternate dark and bright bands are formed on a graph paper pasted on a distant wall. Indicate the correct statement/s. 

(a)  making appropriate measurements, it is possible to determine the diameter of the wire 

(b)  this phenomenon exhibits that light does not follow rectilinear paths 

(c)  this is a case of Fraunhoffer diffraction 

(d)  this is a case of interference of an infinitely large number of Huygens's secondary waves leading to a diffraction pattern

Answer 1

Correct option (a)(b)(c)(d)

Explanation:

The observation indicated in the question are due to diffraction of light. When an obstacle of dimensions comparable to wavelength of light comes in the path of light, it bends around the obstacle and travels forward.

During this process, the secondary wavelets interfere with each other to form a pattern of bright (constructive) and dark (destructive) bands on a screen.

(a)  Condition for the formation of dark band : a sin θ = mλ (here a is the dimensions of the obstacle : diameter of the thread in this case) 

(b)  Diffraction is a wave phenomenon. Diffraction pattern is observed on the screen when light bends around an obstacle.

(c) Diffraction can be studies in two ways : 

(1) Fraunhoffer diffraction : The obstacle, the source and the screen are far away from each other. Plane wave front approximation can be applied 

(2) Fresnel diffraction : The obstacle, the source and the screen are close to each other. Shape of wave front depends on the type of source. (spherical wave front for point source and cylindrical wave fronts for extended source) 

(d)  Diffraction phenomenon inherently involves interference. Secondary wavelets from different waves interfere with each other to form alternate bright and dark bands of varying intensity on the screen.