Total Internal Reflection & Lens Maker's Formula
- Critical Angle ($i_c$): When light travels from denser to rarer medium:
$$\sin i_c = \frac{1}{n}$$
Applications: Optical fibers (core refractive index $>$ cladding), mirages, diamond sparkle.
Lens Maker's Formula:
$$\frac{1}{f} = (n - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$
Optical Instruments: Magnification
- Compound Microscope:
$$m = m_o \times m_e \approx -\frac{L}{f_o}\left(1 + \frac{D}{f_e}\right) \quad (\text{Normal adjustment: } m = -\frac{L}{f_o}\frac{D}{f_e})$$
- Astronomical Telescope:
$$m = -\frac{f_o}{f_e}, \quad \text{Tube Length } L = f_o + f_e$$
