Light

EM Spectrum

unit

language of light

Metric prefix

TGMKhdadcmμnp

$\lambda v=c$

HZ、eV、m、μm、cm……

duality

$$E=h v$$

magnitude

$$m_2-m_1=-2.5 \log \left(\frac{F_2}{F_1}\right)$$

Flux ratio = 100,δm = 5

$$\Delta m=-1.086\left(\frac{\Delta F}{F}\right) \simeq-\frac{\Delta F}{F}$$

band specific

Absolute magnitude ＆Distance modulus

$$m-M=5 \log \left(\frac{d}{10}\right)=5 \log d-5$$(at 10pc)

Apparent distance modulus

$$A_V \approx 0.6 \frac{r}{1000 \mathrm{LY}} \mathrm{mag}$$

surface brightness(per steradian)

$$\mu=m+2.5 \log \theta$$

Photometric Filters

Johnson-Cousins、SDSS、Stromgren、NIR、BGR、narrow band

color index（B-Vthe most commonly uesd）

C-M Diagram

Flux

$$F=\frac{E_{\text {band }}}{\mathrm{d} A \mathrm{~d} t} \quad \quad \operatorname{erg~cm}^{-2} \mathrm{~s}^{-1} \text { or W cm }{ }^{-2}$$

cgs unit

AB magnitude

monochromatic flux

$$\nu F_\nu=\lambda F_\lambda$$

SED

blackbody radiation

$$B_v(T)=\frac{2 h v^3}{c^2} \frac{1}{\mathrm{e}^{h v /(k T)}-1}$$

Wien's displacement law

$$\lambda_{max} = \frac{0.29}{T}(unit = cm)$$

luminosity

Effective temperature

$$L=\int_\pi \mathrm{d} \Omega \int_{4 \pi R^2} \mathrm{~d} A \int_0^{\infty} B_\lambda(T) \mathrm{d} \lambda=4 \pi R^2 \sigma T^4$$

Specific intensity = surface brightness

HR Diagram＆Specture Sequence

OBAFGKM

Atmospheric Extinction

Airmass(should)<=2(altitude>=30deg)

Rayleigh ,Mie scatter

Refraction

Scintillation

Seeing

Dispersion

ISM extinction $$ A_v \approx 0.6\frac{r}{1000LY} mag $$