Home
Class 12
PHYSICS
A long solid cylindrical glass rod of re...

A long solid cylindrical glass rod of refractive index 3/2 is immersed in a liquid of refractive index `(3sqrt(3))/(4)`. The ends of the rod are perpendicular to the central axis of the rod. A light enters one end of the rod at the central axis as shown in the figure . find the maximum value of angle `theta` for which total internal reflection occurs inside the rod?

Text Solution

Verified by Experts

The correct Answer is:
35.26

`"sin"theta= `(mu_(R))/(.^(c)mu_(P))=(3sqrt(3))/(4) xx (sqrt3)/(2) implies Q_(C) = 60^(@)`
`(3sqrt(3))/(4) "sin"theta = (3)/(2)"sin"30^(@) implies "sin"theta = (1)/(sqrt(3)) implies theta = sin^(-1).(1)/(sqrt(3))`
Promotional Banner

Topper's Solved these Questions

  • GEOMETRICAL OPTICS

    ALLEN |Exercise EXERCISE-04[B]|18 Videos

  • GEOMETRICAL OPTICS

    ALLEN |Exercise EXERCISE-05 (A)|35 Videos

  • GEOMETRICAL OPTICS

    ALLEN |Exercise EXERCISE-3|12 Videos

  • CURRENT ELECTRICITY

    ALLEN |Exercise EX.II|66 Videos

  • GRAVITATION

    ALLEN |Exercise EXERCISE 4|9 Videos

Similar Questions

Explore conceptually related problems

(a) Figure 9.32 shows a cross-section of a 'light pipe' made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure. (b) What is the answer if there is no outer covering of the pipe?

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n_(1) surrounded by a medium of lower refractive index n_(2) . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_(1) and n_(2) as shown in the figure . all rays with the angle of incidence i less than a particular value of i_(m) are confined in the medium of refractive index n_(1) . The numerical aperture (NA) of the structure is defined as "sin"i_(m) For two structures namely S_(1) with n_(1) = sqrt(45) //4 "and" n_(2) = 3//2 , "and" S_(2) with n_(1) = 8//5 "and" n_(2) = 7//5 and taking the refractive index of water to be 4/3 and that of air to be 1 , the correct option (s) is (are)

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n_(1) surrounded by a medium of lower refractive index n_(2) . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_(1) and n_(2) as shown in the figure . all rays with the angle of incidence i less than a particular value of i_(m) are confined in the medium of refractive index n_(1) . The numerical aperture (NA) of the structure is defined as "sin"i_(m) If two structures of same cross - sectional area, but different numerical apertures NA_(1) and NA_(2)(NA_(2) lt NA_(1)) are joined longitudinally , the number aperture of the combined structure is

A ray of light is incident normally on one face of 30^(@) - 60^(@) - 90^(@) prism of refractive index 5/3 immersed in water of refractive index 4/3 as shown in figure .

A cubical block of glass of refractive index n_1 is in contact with the surface of water of refractive index n_2. A beam of light is incident on vertical face of the block. After refraction a total internal reflection at the base and refraction at the opposite face take place. The ray emerges at angle theta as shown. The value of theta is given by

A glass wedge with a small angle of refraction theta is placed at a certain distance from a converging lens with a focal length f ,one surface of the wedge being perpendicular to the optical axis of the lens. A point sources S of light is on the other side of the lens at its focus. The rays reflected from the wedge (not from base) produce, after refraction in the lens , two images of the source displaced with respect to each other by d. Find the refractive index of the wedge glass. [Consider only paraxial rays.]

A thin equiconvex lens of glass of refractive index mu=3//2 & of focal length 0.3m in air is sealed into an opening at one end of a tank filled with water (mu=4//3) .On the opposite side of the lens ,a mirror is placed inside the tank on the tank wall perpendicular to the lens axis ,as shown in figure .the separation between the lens and the mirror is 0.8m A small object is placed outside the tank in front of the lens at a distance of 0.9 m form the lens along its axis .Find the position (relative to the lens)of the image of the object fromed by the stsyem.

Find the moment of inertia and radius of gyration of uniform cross-section rod of mass 4 kg and length 90 cm about an axis through one end and perpendicular to the length of rod.

A parallel beam of light is incident from air at an angle alpha on the side of right angled triangular prism of refractive index mu = sqrt(2) . Light undergoes total internal reflection in the prism at the face PR when alpha has a minimum value of 45^@ . The angle theta of the prism is. .

A rod made of glass (mu = 1.5) and of square cross-section is equal is bent into the shape shown in figure. A parallel beam of light falls perpendicurly on the plane flat surface . A . Referring to the diagram, d is the width of a side & R is radius of inner semicircle. find the maximum value of ratio (d)/(R) so that all light entering the glass through surface A emerge from the glass through surface B.

ALLEN -GEOMETRICAL OPTICS-EXERCISE-04[A]
  1. A balloon is rising up along the axis of a concave mirror of radius of...

    Text Solution

    |

  2. A fly F is sitting on a glass slab A , 45 cm thick and of refractive i...

    Text Solution

    |

  3. An air bubble inside a glass slab (µ=1.5) appears 6 cm when viewed fro...

    Text Solution

    |

  4. A slab of glass, of thickness 6 cm and refractive index mu=1.5 is plac...

    Text Solution

    |

  5. A point object is placed 33cm from a convex mirror of curvature radiu...

    Text Solution

    |

  6. A long solid cylindrical glass rod of refractive index 3/2 is immersed...

    Text Solution

    |

  7. Light from a luminious point on the lower face of a rectangular glass ...

    Text Solution

    |

  8. A rod made of glass (mu = 1.5) and of square cross-section is equal is...

    Text Solution

    |

  9. A fish is rising up vertically inside a pond with velocity 4 cm/s and ...

    Text Solution

    |

  10. A ray of light falls on a transparent sphere with centre at C as shown...

    Text Solution

    |

  11. A narrow parallel beam of light is incident on a transparent sphere of...

    Text Solution

    |

  12. A thin equiconvex lens of glass of refractive index mu=3//2 & of focal...

    Text Solution

    |

  13. In the figure shown L is converging lens of focal length 10 cm and M i...

    Text Solution

    |

  14. An object is kept at a distance of 16 cm from a thin lens and the imag...

    Text Solution

    |

  15. A point source of light is kept at a distance of 15cm from a convergi...

    Text Solution

    |

  16. A lens placed between a candle and a fixed screen forms a real tr...

    Text Solution

    |

  17. Consider a 'beam expander' which consists of two converging lenses of ...

    Text Solution

    |

  18. A prism of refractive index sqrt(2) has refractive angle 60^(@) . Find...

    Text Solution

    |

  19. An equilateral prism deviates a ray through23^(@)for two angles of inc...

    Text Solution

    |

  20. The figure shows the path of a ray passing through an equiangular pris...

    Text Solution

    |