In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern on same side. Find the wavelength (in nm) of the light used.
Physics · Wave Optics · young's dubble slit experiments
JEE Mains

Question

In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern on same side. Find the wavelength (in nm) of the light used.

Physics · Wave Optics · young's dubble slit experiments

G1 Physics · Accepted Answer

Let fringe width be β. The 9th bright is at 9β, while the second dark on the same side is at 3β/2. Their separation is 7.5β=7.5 mm, so β=1 mm. Then λ=βd/D=(1×10⁻³)(0.5×10⁻³)/1=5×10⁻⁷ m=500 nm. Answer: 500.