Assertion (A): Diffraction is a sure indication of wave nature.
Reason (R): Only transverse waves can be diffracted.
Diffraction, the bending of waves around obstacles, is a hallmark of wave phenomena, so (A) is true. However, both transverse waves (like light) and longitudinal waves (like sound) can be diffracted, making (R) false.
Assertion (A): We cannot get diffraction pattern from a wide slit illuminated by monochromatic light.
Reason (R): In diffraction pattern, all the bright bands are not of the same intensity.
A diffraction pattern always exists, but for a very wide slit compared to wavelength, it's very narrow and practically unobservable, making (A) practically true. In single-slit diffraction, the central maximum is brightest, and other maxima are less intense, so (R) is true. (R) does not explain (A).
Assertion (A): Diffraction of light is due to dispersion.
Reason (R): Change in path of light around “the corners separates the wavelength of various colours.
Diffraction is the bending of waves around obstacles or through apertures. Dispersion is the phenomenon where a wave's phase velocity depends on its frequency, leading to color separation. These are distinct phenomena. Both assertion and reason are false.
Assertion (A): Sound waves in air cannot be polarised.
Reason (R): Polarisation is the characteristic of light wave only.
Sound waves in air are longitudinal, meaning oscillations are parallel to propagation. Polarisation is a property of transverse waves where oscillations are perpendicular to propagation. Thus, sound cannot be polarised (A is true). Polarisation is characteristic of all transverse waves, not just light (R is false).
Assertion (A): Two polaroids are crossed to each other. When either of them is rotated through \(30^\circ\), then only one eighth of the incident unpolarised light passes through the combination.
Reason (R): According to Malus’s law, \(I \propto cos^2 \theta\) where \(I\) is the resultant intensity transmitted and \(theta\) is the angle between the optical axis of analyser and polariser.
When two crossed polaroids have one rotated by \(30^\circ\), the angle between their axes becomes \(60^\circ\). Incident unpolarised light \(I_0\) reduces to \(I_0/2\) after the first polaroid. By Malus's Law, \(I = (I_0/2) cos^2(60^\circ) = (I_0/2) (1/4) = I_0/8\). Both (A) and (R) are true, and (R) explains (A).