 # 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.

### 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}}