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Optical Instruments - Telescope

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Estimated time: 7 minutes
CBSE: Class 12
Maharashtra State Board: Class 11

Definition: Telescope

An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.

Maharashtra State Board: Class 11

Formula: Magnifying Power of Telescope

  1. \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
  2. M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]
CBSE: Class 12

Key Points: Telescope

Astronomical (Refracting) Telescope:

  • Used to view distant objects.
  • Objective lens (large focal length) forms image A'B' at its focus → acts as object for eyepiece.
  • Eyepiece forms the final virtual, magnified image A''B''.

Magnifying Power: \[MP=\frac{\text{Visual angle with instrument}(\beta)}{\text{Visual angle for unaided eye}(\alpha)}\]

Condition Formula Tube Length
Relaxed eye (normal adjustment) \[m=-\frac{f_a}{f_c}\] \[L=f_o+f_e\]
Distinct vision (D) \[m=-\frac{f_o}{f_e}\left(1+\frac{f_e}{D}\right)\] \[L=f_o+f_e\]

Resolving Power of Telescope:

  • Ability to produce distinct images of two closely spaced objects.
  • Angular separation between two resolvable objects: \[\sin\theta=1.22\frac{\lambda}{d}\]​ (Rayleigh's criterion), where d = aperture.
  • Resolving power is inverse of angular separation.
  • Larger aperture → better resolving power.

Types of Telescope:

  • Refracting telescope: Uses two convex lenses; large objective + small eyepiece.
  • Reflecting telescope: Uses concave mirror to reflect light internally; secondary mirror directs to eyepiece.
  • Keplerian telescope: Converging lens as eyepiece → inverted image.
  • Galilean telescope: Diverging lens as eyepiece → erect image.
  • Magnification of Refracting Telescope: \[M=\frac{f_{o}}{f_{e}}\]

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