Unpolarised light is incident from the air on a plane surface of a material of refractive index 'μ'. At a particular angle of incidence 'i', it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

1. The reflected light is polarised with its electric vector parallel to the plane of incidence.

2. The reflected light is polarised with its electric vector perpendicular to the plane of incidence.

3. $\mathrm{i}={\mathrm{sin}}^{-1}\left(\frac{1}{\mathrm{\mu}}\right)$

4. $\mathrm{i}={\mathrm{tan}}^{-1}\left(\frac{1}{\mathrm{\mu}}\right)$

Subtopic: Polarization of Light |

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In Young's double-slit experiment, the separation d between the slits is 2 mm, the wavelength $\lambda $ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same $\lambda $ and D) the separation between the slits needs to be changed to:-

1. 1.8 mm

2. 1.9 mm

3. 2.1 mm

3. 1.7 mm

Subtopic: Young's Double Slit Experiment |

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The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda}_{1}=4000\stackrel{o}{A}and{\lambda}_{2}=6000\stackrel{o}{A}$ is

(1) 8:27

(2) 9:4

(3) 3:2

(4) 16:81

Subtopic: Resolving Power of Optical Devices |

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Two polaroids ${P}_{1}and{P}_{2}$ are placed with their axis perpendicular to each other. Unpolarised light ${I}_{o}$ is incident on ${P}_{1}$. A third polaroid ${P}_{3}$ is kept in between ${P}_{1}and{P}_{2}$ such that its axis makes an angle ${45}^{\xb0}$ with that of ${P}_{1}$. The intensity of transmitted light through ${P}_{2}$

(a)$\frac{{I}_{o}}{2}$

(b) $\frac{{I}_{o}}{4}$

(c) $\frac{{I}_{o}}{8}$

(d) $\frac{{I}_{o}}{16}$

Subtopic: Polarization of Light |

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The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda}_{1}$=4000 $\stackrel{0}{A}$ and ${\lambda}_{2}=6000\stackrel{0}{A}$ is:

1. 9:4

2. 3:2

3. 16:81

4. 8:27

Subtopic: Resolving Power of Optical Devices |

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Young’s double-slit experiment is first performed in air and then in a medium other than air. It is found that the 8^{th} bright fringe in the medium lies where the 5^{th} dark fringe lies in the air. The refractive index of the medium is nearly:

1. 1.59

2. 1.69

3. 1.78

4. 1.25

Subtopic: Young's Double Slit Experiment |

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Two polaroids P_{1} and P_{2} are placed with their axis perpendicular to each other. Unpolarised light of intensity I_{o} is incident on P_{1}. A third polaroid P_{3} is kept in between P_{1} and P_{2} such that its axis makes an angle 45 ° with that of P_{1}. The intensity of transmitted light through P_{2} is:-

1. $\frac{{I}_{0}}{4}$

2. $\frac{{I}_{0}}{8}$

3. $\frac{{I}_{0}}{16}$

4. $\frac{{I}_{0}}{2}$

Subtopic: Polarization of Light |

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The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio $\frac{{I}_{max}-{I}_{min}}{{I}_{max}+{I}_{min}}$ will be

1.$\frac{\sqrt{n}}{n+1}$

2. $\frac{2\sqrt{n}}{n+1}$

3. $\frac{\sqrt{n}}{{\left(n+1\right)}^{2}}$

4.$\frac{2\sqrt{n}}{{\left(n+1\right)}^{2}}$

Subtopic: Superposition Principle |

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A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength $5\times {10}^{-5}$ cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is

(1) 0.10 cm

(2) 0.25 cm

(3) 0.20 cm

(4) 0.15 cm

Subtopic: Diffraction |

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The intensity at the maximum in Young's double-slit experiment is ${\mathrm{I}}_{0}$ when the distance between two slits is d=5$\lambda $, where $\lambda $ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance D= 10 d?

(1) $\frac{{\mathrm{I}}_{0}}{4}$

(2) $\frac{3}{4}{\mathrm{I}}_{0}$

(3) $\frac{{\mathrm{I}}_{0}}{2}$

(4) ${\mathrm{I}}_{0}$

Subtopic: Young's Double Slit Experiment |

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