### Shortcut Methods

**Typical numericals on Fringe Shift in the Two-hole Interference Equipment for JEE and CBSE board exams:**

**Two-hole interference with monochromatic light:**Shortcut: To calculate the fringe width for monochromatic light, use the formula β = λD/d, where λ is the wavelength of light, D is the distance between the screen and the slits, and d is the distance between the slits.

Formula: β = λD/d β: Fringe width (in meters) λ: Wavelength of light (in meters) D: Distance between the screen and the slits (in meters) d: Distance between the slits (in meters)

**Two-hole interference with white light:**Shortcut: To calculate the overlap of central bright fringes for red and violet light, use the formula Δy = (λ_{red}- λ_{violet}) D/d, where λ_{red}and λ_{violet}are the wavelengths of red and violet light, respectively, D is the distance between the screen and the slits, and d is the distance between the slits.

Formula:
Δy = (λ_{red} - λ_{violet}) D/d
Δy: Overlap of central bright fringes for red and violet light (in meters)
λ_{red}: Wavelength of red light (in meters)
λ_{violet}: Wavelength of violet light (in meters)
D: Distance between the screen and the slits (in meters)
d: Distance between the slits (in meters)

**Effect of wavelength on fringe width:**Shortcut: To calculate the fringe width for different wavelengths of light, use the formula β = λD/d, where λ is the wavelength of light, D is the distance between the screen and the slits, and d is the distance between the slits.

Formula: β = λD/d β: Fringe width (in meters) λ: Wavelength of light (in meters) D: Distance between the screen and the slits (in meters) d: Distance between the slits (in meters)

**Effect of slit separation on fringe width:**Shortcut: To calculate the fringe width for different slit separations, use the formula β = λD/d, where λ is the wavelength of light, D is the distance between the screen and the slits, and d is the distance between the slits.

Formula: β = λD/d β: Fringe width (in meters) λ: Wavelength of light (in meters) D: Distance between the screen and the slits (in meters) d: Distance between the slits (in meters)

**Determination of wavelength using two-hole interference:**Shortcut: To calculate the wavelength of light using two-hole interference, use the formula λ = βD/d, where β is the fringe width, D is the distance between the screen and the slits, and d is the distance between the slits.

Formula: λ = βD/d λ: Wavelength of light (in meters) β: Fringe width (in meters) D: Distance between the screen and the slits (in meters) d: Distance between the slits (in meters)