9.5 Optical Instruments

9.5 Optical Instruments

Simple Microscope (Magnifying Glass)

Magnifying power when the image is at the near point ($D = 25\,\text{cm}$):

$$m = 1 + \frac{D}{f}$$

When the image is at infinity:

$$m = \frac{D}{f}$$

Compound Microscope

$$m = m_o \times m_e = \frac{L}{f_o} \times \frac{D}{f_e}$$

where $L$ is the tube length, $f_o$ is the focal length of the objective, and $f_e$ is the focal length of the eyepiece.

Astronomical Telescope (Normal Adjustment)

$$m = \frac{f_o}{f_e}$$

Tube length: $L = f_o + f_e$

Example

An astronomical telescope has an objective of focal length $100\,\text{cm}$ and an eyepiece of focal length $5\,\text{cm}$. Find the magnifying power and tube length in normal adjustment.

$$m = \frac{f_o}{f_e} = \frac{100}{5} = 20$$ $$L = f_o + f_e = 100 + 5 = 105\,\text{cm}$$