Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $$\pi / 2$$ and $$\pi / 3$$ at points $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively. The difference between the resultant intensities at the two points is $$x I$$. The value of $$x$$ will be ________.

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 $$\times$$ 10^$$-$$2 m towards the slits, the change in fringe width is 3 $$\times$$ 10^$$-$$3 cm. If the distance between the slits is 1 mm, then the wavelength of the light will be ____________ nm.

In a Young's double slit experiment, an angular width of the fringe is 0.35$$^\circ$$ on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $${1 \over \alpha }$$. The value of $$\alpha$$ is ___________.

In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ____________ nm.