Question

In Fraunhofer diffraction, how is the angular width of the central bright fringe affected when slit separation is increased?

Answer 1

Hint: Diffraction is the process by which the ray of light bends when it strikes an obstacle. There are two types of diffraction. That is, Fresnel diffraction and Fraunhofer diffraction. Fresnel diffraction occurs when the light source strikes some obstacle and the waves are spherical here. Fringed images of the objects are also observed. Whereas, in the case of Fraunhofer diffraction plane wave fronts occur. The basic difference between Fresnel and Fraunhofer diffraction is that the light source and screen is at finite difference in case of Fresnel diffraction, whereas The light source and screen are at infinity for Fraunhofer diffraction.

Formula used: In Fraunhofer diffraction,
$d\sin \theta =n\lambda $
  where, d is the width of slit, λ is the wavelength of light used and n is the order of diffraction.

Complete step by step answer:
In Fraunhofer diffraction,
$d\sin \theta =n\lambda $
  where, d is the width of slit, λ is the wavelength of light used and n is the order of diffraction.
For central bright fringe,
 n=1
$\Rightarrow d\sin \theta =\lambda $
Thus angular width of central bright width is,
$2d\sin \theta =2\lambda $
$\Rightarrow 2\sin \theta =\dfrac{2\lambda }{d}$
Thus we can say the angular width of the central bright fringe will decrease as the width of the slit is increased.

Note: There are two types of diffraction. That is, Fresnel diffraction and Fraunhofer diffraction. Fresnel diffraction occurs when the light source strikes some obstacle and the waves are spherical here. Fringed images of the objects are also observed. Whereas, in the case of Fraunhofer diffraction plane wave fronts occurs.The basic difference between Fresnel and Fraunhofer diffraction is that the light source and screen is at finite difference in case of Fresnel diffraction, whereas The light source and screen are at infinity for Fraunhofer diffraction.