Assertion (A): When a width of one of the slits of Young’s double slit experiment is double that of the other than brighter fringes are nine times brighter than the dark fringes.
Reason (R): The amplitude of the wave is proportional to the width of the slit.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In Young's double slit experiment, intensity is proportional to the square of amplitude \(I \propto A^2\). The amplitude \(A\) is proportional to the slit width \(w\). If \(w_1 = 2w_2\), then \(A_1 = 2A_2\). The ratio of maximum to minimum intensity is \(I_{max}/I_{min} = ((A_1+A_2)/(A_1-A_2))^2\). Substituting \(A_1 = 2A_2\), we get \(I_{max}/I_{min} = ((2A_2+A_2)/(2A_2-A_2))^2 = (3A_2/A_2)^2 = 3^2 = 9\). So, (A) is true. (R) is also true, as amplitude is proportional to slit width. And (R) correctly explains (A).
Assertion (A): When tiny circular obstacle is placed in the path of light from some distance, a bright spot is seen at the centre of shadow of the obstacle.
Reason (R): Constructive interference occurs at the centre of the shadow.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) describes the Poisson's spot (or Arago spot) phenomenon, a classical example of diffraction where a bright spot appears in the center of the shadow of an opaque circular object. Reason (R) correctly states that this occurs due to constructive interference of light waves diffracting around the edges of the obstacle and meeting in phase at the center of the shadow. Both are true and R explains A.
Assertion (A): If width of one of the slit in YDSE is slightly increased, then maximum and minimum both Intensity will increase.
Reason (R): Intensity reaching from that slit on screen will slightly increase.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In YDSE, the intensity of light from a slit is proportional to its width \(I \propto w\). Also, amplitude \(A \propto \sqrt{I}\). If one slit's width increases, its amplitude \(A\) increases. The maximum intensity is \(I_{max} = (A_1+A_2)^2\) and minimum intensity is \(I_{min} = (A_1-A_2)^2\). If \(A_1\) increases, both \(I_{max}\) and \(I_{min}\) will increase. Both A and R are true, and R explains A.
Assertion (A): If white light is used in place of monochromatic light in YDSE then central point is white. Although at other places coloured fringes will be obtained.
Reason (R): At centre path difference is zero for all wave lengths. Hence all wave will interfere constructively.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In Young's double slit experiment, the central point has a path difference of zero \(\Delta x = 0\) for all wavelengths \(\lambda\). The condition for constructive interference is \(\Delta x = n\lambda\). For \(n=0\), \(\Delta x = 0\) which is true for all \(\lambda\). Therefore, all colors interfere constructively at the center, resulting in a white fringe. Other fringes are colored due to dispersion. Both are true and R explains A.
Assertion (A): As the separation between the two slits is increased width of fringes decreases.
Reason (R): On increasing separation between two slits, angular separation of fringes decreases.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Fringe width \(beta = \frac{\lambda D}{d}\). As slit separation \(d\) increases, fringe width \(beta\) decreases. Angular fringe width \(theta = \frac{\lambda}{d}\). As \(d\) increases, angular separation \(\theta\) decreases. Thus, R is the correct explanation of A.
Assertion (A): In case of Young double slit experiment width of all fringes were equal.
Reason (R): Angular width of fringes were equal.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In Young's Double Slit Experiment (YDSE), the fringe width \(beta = \frac{\lambda D}{d}\) is constant for all fringes, hence they are of equal width. The angular fringe width \(\theta = \frac{\lambda}{d}\) is also constant. Reason (R) correctly explains Assertion (A).
Assertion (A): If in YDSE, wavelength of light used is increased, angular width remain unchanged only linear width of fringes increases.
Reason (R): Only linear fringe width proportional to wavelength and angular fringe width does not depends on wavelength.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In YDSE, angular fringe width is \(\beta_\theta = \frac{\lambda}{\text{d}}\) and linear fringe width is \(\beta = \frac{\lambda \text{D}}{\text{d}}\). Both are directly proportional to the wavelength \(lambda\). Thus, Assertion (A) is false as angular width also changes. Reason (R) is false as angular width does depend on wavelength.
Assertion (A): The fringe pattern in Young’s double slit experiment is result of both phenomena of interference and diffraction.
Reason (R): Diffraction results from superposition of wavelets of same wavefront.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. The YDSE pattern is an interference pattern modulated by the diffraction pattern from each individual slit.
Reason (R) is true. Diffraction is explained by Huygens' principle, where secondary wavelets from the same wavefront superpose.
Reason (R) defines diffraction but does not explain why both interference and diffraction contribute to the YDSE pattern, so it's not the correct explanation.
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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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).