Ray Optics and Optical Instruments

Optical Instruments

  • Visual angle is the angle subtended by an object at the eye.
  • Myopia means short sightedness, the distant objects are not clearly visible.
  • Hypermetropia means far sightedness, the near objects are not clearly visible.
  • A convex lens is called simple microscope
  • Magnification in simple microscope when final image is formed at least distance of distinct vision \tt m = \left(1 + \frac{D}{f}\right)
  • Magnification when final image at infinity \tt m = \left(\frac{D}{f}\right)
  • Magnification of compound microscope \tt m = \frac{vo}{uo} \left(\frac{D}{ue}\right)
  • Magnification of compound micro scope when final image at ‘D’ is \tt m = - \frac{vo}{uo} \left( 1 + \frac{D}{fe}\right)
  • Length of compound microscope LD = Vo + Ue
  • Magnification of compound microscope when final image formed at infinity \tt m = \frac{vo}{uo} \cdot \left(\frac{D}{fe}\right)
  • Length of compound microscope L = vo + fe
  • Magnification of Astronomical Telescope \tt M = - \frac{fo}{ue}
  • Magnification at D MD = \tt - \frac{fo}{fe} \left(1 + \frac{fe}{D}\right)
  • Length of Astronomical Telescope LD = fo + ue
  • Magnification at ∞ M = \tt - \frac{fo}{fe}
  • Length of Astronomical Telescope \tt L_{\infty} = fo + fe
  • Terrestrial Telescope magnification \tt m = \frac{fo}{ue}
  • Magnification of ‘D’ \tt M_{D} = \frac{fo}{fe} \left(1 + \frac{fe}{D}\right)
  • Length LD = fo + 4f + ue
  • Magnification \tt M_{\infty} = \frac{fo}{fe}
  • Length L = fo + 4f + fe
  • The telescope in which the objective is a curved mirror is called Reflecting Telescope.

Viewing objects: Eyes as an optical instrument

Microscopes and Telescopes

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1. It is an optical instrument used to see very small object. It's magnifying power is given by
\tt m = \frac{Visual \ angle \ with \ instrument \ (\beta)}{Visual \ angle \ when \ object \ is \ placed \ at \ least \ distance \ of \ distinct \ vision (\alpha)}

2. Magnification when final image is formed at D and ∞ (i.e., mD and m): m_{D} = \left[1 + \frac{D}{f}\right]_{max} \ {\tt and} \ m_{\infty} = \left[\frac{D}{f}\right]_{min}

3. If lens is kept at a distance a from the eye then m_{D} = 1 + \frac{D - a}{f} \ {\tt and} \ m_{\infty} = \frac{D - a}{f}

4. Final image is forned at D : Magnification m_{D} = -\frac{v_{0}}{u_{0}}\left[1 + \frac{D}{f_{e}}\right] and length of the microscope tube (distance between two lenses) is LD = v0 + ue

5. Telescope (Refracting Type) Magnification: m_{D} = -\frac{f_{0}}{f_{e}}\left[1 + \frac{f_{e}}{D}\right] \ {\tt and} \ m_{\infty} = -\frac{f_{0}}{f_{e}}