Practice NEET Young's Double Slit Experiment Questions
Question 31:
easy
Assertion (A): In a YDSE, the two slits are at distance ‘a’ apart. Interference pattern is observed on a screen at a distance D from the slits. At a point on the screen which is directly opposite to the slit, a dark fringe is observed. Then the wavelength of wave is proportional to square of distance between slits.
Reason (R): The light ray coming from two slits do not interfere at the screen.
Assertion (A) is true. If a dark fringe occurs at \(y = a/2\) (point opposite one slit), the path difference is \(a^2/(2D)\). For a dark fringe, \(a^2/(2D) = (n + 1/2)\lambda\), implying \(lambda \propto a^2\).
Reason (R) is false. The core principle of YDSE is the interference of light waves from two coherent slits, which produces the observed pattern on the screen.
Assertion (A): In a Young’s double slit experiment if slit separation is slightly greater than (nl) if (n) is integer No. of maxima on screen is (2n + 1) & no of minima is (2n).
Reason (R): In Young’s double slit experiment path difference at different position are different.
Assertion (A) is true. If slit separation (d) is slightly greater than (nlambda), there will be (2n+1) maxima and (2n) minima. Reason (R) is also true as path difference (Delta x = d sintheta) varies with position. However, (R) does not explain the specific count of fringes in (A).
Assertion (A): In standard YDSE experiment if upper slit is slightly moved downward then central maxima shifts downward.
Reason (R): Fringe width in such case will increase.
Assertion (A) is true; moving a slit shifts the central maxima in the direction of the movement. Reason (R) is false. Fringe width \(\beta = \frac{\lambda D}{d}\) depends on wavelength, screen distance, and slit separation, none of which change.
Assertion (A): If the phase difference between the light waves emerging from the slits of the Young’s experiment is \(\pi\) radian, then central fringe will be dark.
Reason (R): Phase difference is equal to \(\frac{2\pi}{\lambda}\) times the effective path difference.
Assertion (A) is true. An initial \(\pi\) phase difference means destructive interference at the central point (where path difference is zero). Reason (R) is also true, as \(\Delta\phi = \frac{2\pi}{\lambda} \Delta x). (R) explains how phase difference relates to path difference, justifying (A).
Assertion (A): In YDSE central maxima means the maxima formed with zero optical path difference. It may be formed anywhere on the screen.
Reason (R): In an interference pattern, whatever energy disappears at the minimum, appears at the maximum.
Both Assertion (A) and Reason (R) are true statements. Central maxima is indeed defined by zero path difference, and its location can be shifted. Interference redistributes energy, meaning energy is conserved. However, (R) does not explain the definition or position of central maxima in (A).
Assertion (A): In Young’s double slit experiment if intensity of each source is \(I_0\) then minimum and maximum intensity is zero and \(4I_0\) respectively.
Reason (R): In Young’s double slit experiment energy conservation is not followed.
In YDSE with coherent sources of intensity (I_0) each, \(I_{\text{min}} = (\sqrt{I_0} - \sqrt{I_0})^2 = 0\) and \(I_{\text{max}} = (\sqrt{I_0} + \sqrt{I_0})^2 = 4I_0\). Thus, A is true. Energy is conserved in interference; it's redistributed, not destroyed. Thus, R is false.
Assertion (A): In standard YDSE set up with visible light, the position on screen where phase difference is zero appears bright.
Reason (R): In YDSE set up amplitude of electromagnetic field at central bright fringe is not varying with time.
A zero phase difference signifies constructive interference, resulting in a bright fringe. Hence, A is true. The amplitude of the electromagnetic field at the central bright fringe remains constant over time in a stable interference pattern, but this is not the reason for it being bright due to zero phase difference. Hence, R is true but not the correct explanation for A.
Assertion (A): In Young’s experiment, the fringe width for dark fringes is different from that for bright fringes.
Reason (R): In Young’s double slit experiment with a source of white light, only black and white fringes are observed.
In YDSE, the fringe width is given by \(\beta = \frac{\lambda D}{d}\), which is independent of whether the fringe is bright or dark. Hence, A is false. With white light, a central bright white fringe is formed, and then colored fringes are observed, not just black and white. Hence, R is false.
Assertion (A): If a glass slab is placed in front of one of the slits, then fringe width will decrease.
Reason (R): Glass slab will produce no path difference.
Placing a glass slab in front of one slit causes a path difference of \(t(\mu - 1)\) and shifts the entire fringe pattern but does not alter the fringe width \(\beta = \frac{\lambda D}{d}\). Thus, A is false. A glass slab indeed introduces an additional optical path difference. Thus, R is false.
Assertion (A): If two sodium lamps are used illuminating two pinholes, interference fringes will not be observed.
Reason (R): Light waves coming from an ordinary source like sodium lamp are unpolarised in nature.
Assertion (A) is true: Two independent sources (like sodium lamps) are incoherent, meaning they do not maintain a constant phase relationship, thus cannot produce a stable interference pattern. Reason (R) is true: Light from ordinary sources like sodium lamps is unpolarised. However, incoherence is the primary reason for no interference, not the unpolarised nature. Thus, (R) is not the correct explanation for (A).