Question

Two straight and narrow parallel slits 1mm apart are illuminsted by monochromatic light. Fringes formed on the screen held at distance of 100cm from the slit are 0.50mm apart. What is the wavelength is used

Answer 1

distance between two parallel slits , d = 1mm = 10^-3 m

distance between slits and screen , D = 100cm = 1m

fringe width, $\beta$ 0.5 mm = 5 × 10^-3 m

we know,

fringe width, $\beta=\frac{\lambda D}{d}$

or, 0.5 × 10^-3 = $\lambda$ × 1/10^-3

or, 0.5 × 10^-3 × 10^-3 = $\lambda$

or, 0.5 × 10^-6 = 5000 × 10^-10m = $\lambda$

hence, $\lambda$ = 5000 A°

so, wavelength of monochromatic light is 5000 A°