Crown Glass Prism
\(A=60°, n_{\text{red}}=1.513, n_{\text{violet}}=1.532\), dispersion ≈ 2-3°
プリズム分散計算機
プリズムが白色光を虹のスペクトラムに分離する方法を探索。偏差と角分散を計算
Prism Dispersion Visualization
White light enters the prism and separates into its spectrum colors (ROYGBIV). Violet light deviates the most.
結果
値を入力して計算をクリックして結果を表示してください。
Theory & Formula
Dispersion is the phenomenon where white light separates into its component colors when passing through a prism.
Why Dispersion Occurs:
- Wavelength Dependence: Refractive index varies with wavelength
- Violet Light: Shorter wavelength (≈400nm), higher n, bends more
- Red Light: Longer wavelength (≈650nm), lower n, bends less
- ROYGBIV: Red, Orange, Yellow, Green, Blue, Indigo, Violet
Deviation Through Prism:
- \(\delta = i_1 + e_2 - A\) (where \(e_2\) is emergence angle)
- Minimum deviation occurs when ray passes symmetrically
- At minimum deviation: \(i_1 = e_2\) and \(r_1 = r_2 = A/2\)
- \(\delta_{\text{min}} = 2i_1 - A\), and \(n = \frac{\sin[(A + \delta_{\text{min}})/2]}{\sin(A/2)}\)
Angular Dispersion:
- \(\Delta\delta = \delta_{\text{violet}} - \delta_{\text{red}}\)
- Depends on \((n_v - n_r)\) called dispersive power
- Flint glass has higher dispersion than crown glass
- Used in spectroscopy to analyze light composition
Applications:
- Rainbows (water droplets)
- Spectroscopy and spectrum analysis
- Optical instruments (spectrometers)
- Understanding atomic emission/absorption
\(\delta = i_1 + e_2 - A\)
Worked Examples
Flint Glass Prism
Higher dispersion, \(n_{\text{violet}}-n_{\text{red}} \approx 0.03\), creates wider spectrum
Rainbow Formation
Water droplets act as prisms, dispersing sunlight