Question

In Fraunhofer diffraction pattern due to a single slit, the slit of width $ 0.1\,\,mm $ is illuminated by monochromatic light of wavelength $ 600\,\,nm $ . What is the ratio of separation between the central maximum and first secondary minimum to the distance between screen and the slit?
(A) $ 6 \times {10^{ - 3}}\,\,m $
(B) $ 0.1\,\,m $
(C) $ 6\,\,m $
(D) $ 100\,\,m $

Answer 1

Hint
 In the field of optics, the Fraunhofer diffraction equation is used to shape the diffraction of waves when the diffraction pattern is observed at a long distance from the diffracting object, and also when it is observed at the focal plane of an imaging lens.
Fraunhofer diffraction formula is given as;
 $ \alpha = \dfrac{{2\lambda }}{W} $
Where, $ \alpha $ denotes the Fraunhofer diffraction, $ \lambda $ denotes the wavelength of the monochromatic light source, $ W $ denotes the width of the single slit.

Complete step by step answer
The data’s that are given in the problem are;
The wavelength of the monochromatic light source, $ \lambda = 600\,\,nm $ .
The width of the single slit is, $ W = 0.1\,\,mm $ .
Fraunhofer diffraction pattern due to a single slit formula is given as;
 $ \alpha = \dfrac{{2\lambda }}{W} $
Substitute the values of wavelength of the monochromatic light source and the width of the single slit in the above Fraunhofer diffraction formula;
 $ \alpha = \dfrac{{2 \times \left( {600 \times {{10}^{ - 9}}\,\,m} \right)}}{{0.1 \times {{10}^{ - 3}}\,\,m}} $
Changing the notations into meter for easier calculation;
 $ \alpha = 6 \times {10^{ - 3}}\,\,m $
Therefore, separation between the central maximum and first secondary minimum to the distance between screen and the is given as $ \alpha = 6 \times {10^{ - 3}}\,\,m $ .
Hence, the option (A) $ \alpha = 6 \times {10^{ - 3}}\,\,m $ is the correct answer.

Note
In the double-slit experiment it is an illustration that light and matter can exhibit attributes of both traditionally explained waves and particles; furthermore, it exhibits the radically prospect nature of quantum mechanical phenomena.