The ratio of intensities at two points on the screen in Young's double slit experiment when waves from the two slits have a path difference of zero and $\lambda/4$ is ($\lambda$ is the wavelength of light used) ($\cos 0^\circ = 1$, $\cos\pi/2 = 0$)

In Young's double slit experiment, the distance between the slits is 3 mm and the slits are 2m away from the screen. Two interference patterns can be obtained on the screen due to light of wavelength 480 nm and 600 nm respectively. The separation on the screen between the $5^{\text{th}}$ order bright fringes on two interference patterns is

A double slit experiment is immersed in water of refractive index $1.33$. The slit separation is 1 mm, distance between slit and screen is $1.33$ m. The slits are illuminated by light of wavelength 6300 $\text{\AA}$. The fringe width is

Light of wavelength $\lambda$ is incident on a single slit of width 'a' and the distance between slit and screen is 'D'. In diffraction pattern, if slit width is equal to the width of the central maximum then 'D' is equal to