Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of…

Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width $\displaystyle 2 \mu \mathrm{~m}$ each in an opaque material are separated by a distance of $\displaystyle 6 \mu \mathrm{~m}$. Monochromatic light of wavelength $\displaystyle 450$ nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen.

The number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :

$\displaystyle 2$ (B) $\displaystyle 3$ (C) $\displaystyle 4$ (D) $\displaystyle 6$ (ii) The number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :

$\displaystyle 1$ (B) $\displaystyle 2$ (C) $\displaystyle 3$ (D) $\displaystyle 4$ (iii) (a) If instead of $\displaystyle 450$ nm light, another light of wavelength $\displaystyle 680$ nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :

$\displaystyle 2$ (B) $\displaystyle 4$ (C) $\displaystyle 6$ (D) $\displaystyle 9$

Consider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle $\displaystyle \theta$ equal to :

$\displaystyle \sin ^{-1}(0 \cdot 12)$

$\displaystyle \sin ^{-1}(0.225)$

$\displaystyle \sin ^{-1}(0.32)$

$\displaystyle \sin ^{-1}(0 \cdot 45)$

The number of bright fringes formed due to interference on $\displaystyle 1$ m of screen placed at $\displaystyle \frac{4}{3} \mathrm{~m}$ away from the slits is :

$\displaystyle 2$ (B) $\displaystyle 3$ (C) $\displaystyle 6$ (D) $\displaystyle 10$