A plano-convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ_{1} and μ_{2 }and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

1. $\frac{\mathrm{R}}{2({\mathrm{\mu}}_{1}-{\mathrm{\mu}}_{2})}$

2. $\frac{\mathrm{R}}{({\mathrm{\mu}}_{1}-{\mathrm{\mu}}_{2})}$

3. $\frac{2\mathrm{R}}{({\mathrm{\mu}}_{2}-{\mathrm{\mu}}_{1})}$

4. $\frac{\mathrm{R}}{2({\mathrm{\mu}}_{1}+{\mathrm{\mu}}_{2})}$

Subtopic: Lens Makers' Formula |

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For a normal eye, the cornea of the eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:

1. 2.5 cm

2. 1.67 cm

3. 1.5 cm

4. 5 cm

Subtopic: Human Eye |

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When a biconvex lens of glass having a refractive index of 1.47 is dipped in a liquid, it acts as a plane sheet of glass. The liquid must have a refractive index:

1. equal to that of glass.

2. less than one.

3. greater than that of glass.

4. less than that of glass.

Subtopic: Lens Makers' Formula |

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A ray of light is incident at an angle of incidence, i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu $, the angle of incidence i, is nearly equal to

1. $\mu $A

2. $\frac{\mu A}{2}$

3. $A/\mu $

4. $A/2\mu $

Subtopic: Prisms |

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A concave mirror of the focal length ${f}_{1}$ is placed at a distance of d from a convex lens of focal length ${f}_{2}$. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance d must be equal to:

1. ${f}_{1}+{f}_{2}$

2. $-{f}_{1}+{f}_{2}$

3. $2{f}_{1}+{f}_{2}$

4. $-2{f}_{1}+{f}_{2}$

Subtopic: Reflection at Spherical Surface |

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The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal length of the lenses is :

1. 10 cm, 10 cm

2. 15 cm, 5 cm

3. 18 cm, 2 cm

4. 11 cm, 9 cm

Subtopic: Telescope |

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A biconvex lens $\left(\mathrm{\mu}=1.5\right)$ has a radius of curvature of magnitude 20 cm. Which one of the following options, best describes, the image formed of an object of height 2 cm placed 30 cm from the lens?

1. Virtual, upright, height = 0.5 cm

2. Real, inverted, height = 4 cm

3. Real, inverted, height = 1 cm

4. Virtual, upright, height = 1 cm

Subtopic: Lenses | Lens Makers' Formula | Refraction at Curved Surface |

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Which of the following is not due to total internal reflection?

1. Difference between apparent and real depth of the pond

2. Mirage on hot summer days

3. Brilliance of the diamond

4. Working of optical fibre

Subtopic: Total Internal Reflection |

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A ray of light travelling in a transparent medium of refractive index $\mu $ falls on a surface separating the medium from the air at an angle of incidence of 45 °. For which of the following value of $\mu $, the ray can undergo total internal reflection?

1. $\mu =1.33$

2. $\mu =1.40$

3. $\mu =1.50$

4. $\mu =1.25$

Subtopic: Total Internal Reflection |

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A lens having focal length f and aperture of diameter d forms an image of intensity I . An aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. The focal length of lens and intensity of the image now will be respectively:

1. f and $\frac{\mathrm{I}}{4}$

2. $\frac{3f}{4}and\frac{I}{2}$

3. f and $\frac{3I}{4}$

4. $\frac{f}{2}and\frac{I}{2}$

Subtopic: Lenses |

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