In Young's experiment, the distance between two slits is 1 mm and the distance between two consecutive bright fringes is 0.03 cm. Now, on displacing the screen away from the slits by 50 cm, the distance between two consecutive dark fringes is doubled. Find the wavelength of light used.

Explanation

When distance between slit and screen is `D_(1)=D,` distance between two consecutive bright fringes,
`beta_(1)=(lamdaD_(1))/(d)" "....(1)`
When distance between slit and screen is `D_(1)=D+50` cm, distance between two consecutive bright fringes,
`beta_(2)=(lamdaD_(2))/(d)" "....(2)`
`beta_(1)-beta_(2)=(lamda)/(d)(D_(2)-D_(1))`
`:.beta_(2)-beta_(1)=(lamda)/(d)(D+50-D)`
`:.2beta_(1)-beta_(1)=(50lamda)/(d)`
`:.0.06-0.03=(50xxlamda)/(0.1)`
`:.(0.03xx0.1)/(50)=lamda` `:.0.6xx10^(-4)=lamda`
`:.lamda-6xx10^(-5)cm-6,000xx10^(-8)cm`
`:.lamda=6000Å`