Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is ${F}_{1}$. When the space between the two lenses is filled with glycerin which has the same refractive index as that of glass ($\mu =1.5$), then the equivalent focal length is ${F}_{2}$. The ratio ${F}_{1}:{F}_{2}$ will be:

1. 3: 4

2. 2: 1

3. 1: 2

4. 2: 3

Subtopic: Lens Makers' Formula |

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A double convex lens has a focal length of 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5.

1. 100 cm, 50 cm

2. 25 cm, 50 cm

3. 18.75 cm, 37.5 cm

4. 50 cm, 100 cm

Subtopic: Lens Makers' Formula |

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Two identical thin plano-convex glass lenses (refractive index = 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is:

1. -20 cm

2. -25 cm

3. -50 cm

4. 50 cm

Subtopic: Lens Makers' Formula |

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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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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 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 by 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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A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will:

1. become zero.

2. become infinite.

3. become small, but non-zero.

4. remain unchanged.

Subtopic: Lens Makers' Formula |

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A plane convex lens (µ = 1.5) has a radius of curvature 10 cm. It is silvered on its plane surface. The focal length of the lens after silvering is:

1. 10 cm

2. 20 cm

3. 15 cm

4. 25 cm

Subtopic: Lens Makers' Formula |

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