Shortcut Methods
Shortcuts & Tricks for Numerical Problems in Optics
Diffraction:
- Single Slit:
- For the central maximum:
- For the first secondary maxima (on either side of central maxima):
where (\lambda) is the wavelength, (L) is the distance between the slit and the screen, and (d) is the slit width.
- Multiple Slits:
- Use
Interference:
-
Double-Slit:
-
Path difference for constructive interference:
-
Fringe spacing:
where (\Delta y) is the distance between adjacent bright fringes, (L) is the distance to the screen, and (\theta) is the angle from the central maximum.
- Thin Films:
-For constructive interference:
Polarization:
- Brewster’s Angle:
where (\theta_B) is Brewster’s angle, and (n_1) and (n_2) are the refractive indices of the two media.
- Intensity of Transmitted Light:
where (I_t) is the intensity of transmitted light, (I_0) is the intensity of incident light, and (θ) is the angle between the polarization direction of the incident light and the transmission axis of the polarizer.
Note: These are just a few general shortcuts and tricks for numerical problems in optics. Depending on the specific question, you may need to use a combination of these methods and apply other relevant equations and concepts from optics.
