Chapter 24

Assertion A famous painting was painted by not using brush strokes in the usual manner, but rather a myriad of small colour dots. In this painting the colour you see at any given place on the painting changes as you move away. Reason The angular separation of adjacent dots changes with the distance from the painting.

A beam of light consisting of two wavelengths 650 \(\mathrm{nm}\) and \(520 \mathrm{~nm}\) is used to illuminate the slit of a Young's double slit experiment. Then the order of the bright fringe of the longer wavelength that coincide with a bright fringe of the shorter wavelength at the least distance from the central maximum is (a) 1 (b) 2 (c) 3 (d) 4

Assertion In Young's experiment, the fringe width for dark fringes is same from that for white fringes. Reason In Young's double slit experiment, when the fringes are performed with a source of white light, then only black and bright fringes are observed.

Assertion Thin films such as soap bubble or a thin layer of oil on water show beautiful colours when illuminated by white light. Reason It happens due to the interference of light reflected from the upper surface of the thin film.

In Young's double slit experiment, the 8 th maximum with wavelength \(\lambda_{1}\) is at a distance, \(d_{1}\) from the central maximum and the 6 th maximum with wavelength \(\lambda_{2}\) is at a distance, \(d_{2}\). Then, \(d_{1} / d_{2}\) is equal to (a) \(\frac{4}{3}\left(\frac{\lambda_{2}}{\lambda_{1}}\right)\) (b) \(\frac{4}{3}\left(\frac{\lambda_{1}}{\lambda_{2}}\right)\) (c) \(\frac{3}{4}\left(\frac{\lambda_{2}}{\lambda_{1}}\right)\) (d) \(\frac{3}{4}\left(\frac{\lambda_{1}}{\lambda_{2}}\right)\)

Assertion Corpuscular theory fails in explaining the velocities of light in air and water. Reason According to corpuscular theory, light should travel faster in denser media than in rarer media.

Light of wavelength \(500 \mathrm{~nm}\) is used to form interference pattern in Young's double slit experiment. A uniform glass plate of refractive index \(1.5\) and thickness \(0.1 \mathrm{~mm}\) is introduced in the path of one of the interfering beams. The number of fringes which will shift the cross wire due to this is (a) 100 (b) 200 (c) 300 (d) 400

Air has refractive index \(1.003 .\) The thickness of air column, which will have one more wavelength of yellow light \((6000 \AA)\) than in the same thickness of vacuum is (a) \(2 \mathrm{~mm}\) (b) \(2 \mathrm{~cm}\) (c) \(2 \mathrm{~m}\) (d) \(2 \mathrm{~km}\)

Air has refractive index \(1.003 .\) The thickness of air column, which will have one more wavelength of yellow light \((6000 \AA)\) than in the same thickness of vacuum is (a) \(2 \mathrm{~mm}\) (b) \(2 \mathrm{~cm}\) (c) \(2 \mathrm{~m}\) (d) \(2 \mathrm{~km}\)

Assertion No diffraction is produced in sound waves near a very small opening. Reason For diffraction to take place the aperture of opening should be of the same order as wavelength of the waves.

Plane microwaves are incident on a long slit having a width of \(5 \mathrm{~cm}\). The wavelength of the microwaves if the first minimum is formed at \(30^{\circ}\) is (a) \(2.5 \mathrm{~cm}\) (b) \(2 \mathrm{~cm}\) (c) \(25 \mathrm{~cm}\) (d) \(2 \mathrm{~mm}\)

Assertion In Young's experiment, for two coherent sources, the resultant intensity given by \(I=4 I_{0} \cos ^{2} \frac{\phi}{2}\) Reason Ratio of maximum and minimum intensity \(\frac{I_{\mathrm{max}}}{I_{\min }}=\frac{\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}}{\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}}\)

A plane wave of wavelength \(6250 \AA\) is incident normally on a slit of width \(2 \times 10^{-2} \mathrm{~cm}\). The width of the principal maximum on a screen distant \(50 \mathrm{~cm}\) will be (a) \(312.5 \times 10^{-1} \mathrm{~cm}\) (b) \(312.5 \times 10^{-4} \mathrm{~cm}\) (c) \(312 \mathrm{~cm}\) (d) \(312.5 \times 10^{-5} \mathrm{~cm}\)

A plane wave of wavelength \(6250 \mathrm{~A}\) is incident normally on a slit of width \(2 \times 10^{-2} \mathrm{~cm}\). The width of the principal maximum on a screen distant \(50 \mathrm{~cm}\) will be (a) \(312.5 \times 10^{-3} \mathrm{~cm}\) (b) \(312.5 \times 10^{-4} \mathrm{~cm}\) (c) \(312 \mathrm{~cm}\) (d) \(312.5 \times 10^{-5} \mathrm{~cm}\)

Assertion For best contrast between maxima and minima in the interference pattern of Young's double slit experiment, the intensity of light emerging out of the two slits should be equal. Reason The intensity of interference pattern is proportional to square of amplitude.

Light of wavelength \(6000 \AA\) is incident on a single slit. The first minimum of the diffraction pattern is obtained at \(4 \mathrm{~mm}\) from the centre. The screen is at a distance of \(2 \mathrm{~m}\) from the slit. The slit width will be (a) \(0.3 \mathrm{~mm}\) (b) \(0.2 \mathrm{~mm}\) (c) \(0.15 \mathrm{~mm}\) (d) \(0.1 \mathrm{~mm}\)

The Fraunhofer diffraction pattern of a single slit is formed in the focal plane of a lens of focal length \(1 \mathrm{~m}\). The width of slit is \(0.3 \mathrm{~mm}\). If third minimum is formed at a distance of \(5 \mathrm{~mm}\) from central maximum, then wavelength of light will be (a) \(5000 \mathrm{~A}\) (b) \(2500 \mathrm{~A}\) (c) \(7500 \AA\) (d) \(8500 \mathrm{~A}\)

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of light from one slit is double of that from other slit. If, \(I_{m}\) be the maximum intensity, the resultant intensity \(I\) when they interfere at phase difference \(\phi\), is given by [AIEEE 2012] (a) \(\frac{l_{m}}{9}(4+5 \cos \phi)\) (b) \(\frac{I_{m}}{3}\left(1+\cos ^{2} \frac{\phi}{2}\right)\) (c) \(\frac{l_{\mathrm{m}}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right)\) (d) \(\frac{l_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right)\)

What should be refractive index of a transparent medium to be invisible in vacuum? (a) 1 (b) \(<1\) (c) \(>1\) (d) None of these

What should be refractive index of a transparent medium to be invisible in vacuum? (a) 1 (b) \(<1\) (c) \(>1\) (d) None of these

Which of the following phenomena is not common to sound and light waves? (a) Interference (b) Diffraction (c) Coherence (d) Polarisation

Which of the following phenomena is not common to sound and light waves? (a) Interference (b) Diffraction (c) Coherence (d) Polarisation

A thin air film is formed by putting the convex surface of a pleno-convex lens over a plane glass plate. With monochromatic source of light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement I When light reflects from the air glass plate interface, the reflected want suffers a phase change of \(\pi\). Statement II The centre of the interface pattern is dark.

What is the Brewster's angle for air to glass transition? (Refractive index of glass \(=1.5\) ) \([\) NCERT] (a) \(15^{\circ} \overline{27}\) (b) \(36^{\circ} 27^{\prime}\) (c) \(50^{\circ} 16^{\prime}\) (d) \(56^{\circ} 18^{\prime}\)

An unpolarised beam of intensity \(2 \alpha^{2}\) passes through a thin polaroid. Assuming zero absorption in the polaroid, the instensity of emergent plane polarised light is (a) \(2 a^{2}\) (b) \(a^{2}\) (c) \(\sqrt{2} a^{2}\) (d) \(\frac{a^{2}}{2}\)

\(80 \mathrm{~g}\) of impure sugar, when dissolved in a litre of water gives an optical rotation of \(9.9^{\circ}\), when placed in a tube of length \(20 \mathrm{~cm}\). If, the specific rotation of sugar is \(66^{\circ}\), then concentration of sugar solution will be (a) \(80 \mathrm{gL}^{-1}\) (b) \(75 \mathrm{gL}^{-1}\) [c) \(65 \mathrm{gL}^{-1}\) (d) \(50 \mathrm{gL}^{-1}\)