$7$The principle of superposition is used to understand the phenomenon of interference of light waves. The principle states that at a particular point, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each wave. Light waves from two coherent sources produce interference pattern. Thomas Young devised a way to obtain two coherent sources using two identical pinholes ( $\displaystyle \mathrm{S}_{1}$ and $\displaystyle \mathrm{S}_{2}$ ) illuminated by a single monochromatic pinhole source S . Using these sources in his experiment known as Young's double slit experiment, Young studied the interference pattern. The pattern consists of alternate bright and dark fringes. The distance between two successive bright or dark finges depends on the distance between $\displaystyle \mathrm{S}_{1}$ and $\displaystyle \mathrm{S}_{2}$, the distance of the screen from the plane of $\displaystyle \mathrm{S}_{1} \mathrm{~S}_{2}$ and the wavelength of light used. I. Consider the following waves :

(i)$\displaystyle \mathrm{y}_{1}=\mathrm{a} \sin \omega \mathrm{t}$(ii)$\displaystyle \mathrm{y}_{2}=\mathrm{a} \sin 2 \omega \mathrm{t}$(iii)$\displaystyle \mathrm{y}_{3}=\mathrm{a} \sin (2 \omega \mathrm{t}+\phi)$(iv)$\displaystyle \mathrm{y}_{4}=\mathrm{a} \sin \left(4 \omega \mathrm{t}+\frac{\pi}{2}\right)$ Which pair of the waves coming from two sources $\displaystyle \mathrm{S}_{1}$ and $\displaystyle \mathrm{S}_{2}$ will produce interference ?

(A) (i) and (ii) (B) (ii) and (iii) (C) (iii) and (iv) (D) (iv) and (i) II. Two light waves of the same intensity $\displaystyle \mathrm{I}_{0}$ each, having a path difference of $\displaystyle \lambda / 4$, emanating from two coherent sources, meet at a point. The resultant intensity at the point will be (A) Zero (B) $\displaystyle \mathrm{I}_{0}$ (C) $\displaystyle 2 \mathrm{I}_{0}$ (D) $\displaystyle 4 \mathrm{I}_{0}$ III. Vandana performs Young's double slit experiment by using orange, green and red lights successively. If the fringe widths measured in the three cases are $\displaystyle \omega_{1}, \omega_{2}$ and $\displaystyle \omega_{3}$ respectively, then which of the following is correct ? (A) $\displaystyle \omega_{2}>\omega_{1}>\omega_{3}$ (B) $\displaystyle \omega_{1}>\omega_{2}>\omega_{3}$ (C) $\displaystyle \omega_{2}>\omega_{3}>\omega_{1}$ (D) $\displaystyle \omega_{3}>\omega_{1}>\omega_{2}$ IV. In a Young's double slit experiment, the slit separation is 0.8 mm and the interference pattern is obtained on a screen kept 50 cm from the plane of the slits $\displaystyle \mathrm{S}_{1}$ and $\displaystyle \mathrm{S}_{2}$. If the first bright fringe is formed 0.4 mm from the central maximum, the wavelength of light used is (A) 480 nm (B) 560 nm (C) 640 nm (D) 680 nm V. Consider the effect on the angular separation of the fringes in a Young's double slit experiment due to the following operations :

(i)the screen is moved away from the plane of the slits,(ii)the separation between the two slits is increased till fringes are observed. Which of the following options is correct ?

(A) It remains constant in both cases. (B) It decreases in both cases. (C) It remains constant in (i) but decreases in (ii). (D) It decreases in (i) but remains constant in (ii).

Physics · Wave Optics