Find the range of frequency of light that is visible to an average human being $(400 \mathrm{nm}<\lambda <700 \mathrm{nm})$.

The wavelength of sodium light in air is $589 \mathrm{nm}$

$\left(a\right)$ Find its frequency in air.

$\left(b\right)$ Find its wavelength in water (refractive index $=1.33$).

$\left(c\right)$ Find its frequency in water.

$\left(d\right)$ Find its speed in water.

Two narrow slits emitting light in phase are separated by a distance of $1.0 \mathrm{cm}$. The wavelength of the light is $5.0\times {10}^{-7} \mathrm{m}$. The interference pattern is observed on a screen placed at a distance of $1.0 \mathrm{m}$.
$\left(a\right)$ Find the separation between the consecutive maxima. Can you expect to distinguish between these maxima?

$\left(b\right)$ Find the separation between the sources which will give a separation of $1.0 \mathrm{mm}$ between the consecutive maxima.

In a double slit interference experiment, the separation between the slits is $1.0 \mathrm{mm}$, the wavelength of light used is $5.0\times {10}^{-7} \mathrm{m}$ and the distance of the screen from the slits is $1.0 \mathrm{m}$.

$\left(a\right)$ Find the distance of the center of the first minimum from the center of the central maximum.

$\left(b\right)$ How many bright fringes are formed in one centimeter width on the screen?