NCERT Solutions for Chapter: Wave Optics, Exercise 4: LA

Figure shows a two slit arrangement with a source which emits unpolarized light. $\mathrm{P}$ is a polariser with axis whose direction is not given. If $I_0$ is the intensity of the principal maxima when no polariser is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.

A small transparent slab containing material of $\mathrm{\mu } =1.5$ is placed along ${\mathrm{AS}}_2$. What will be the distance from $O$ of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab.

The optical properties of a medium are governed by the relative permittivity $\left({\epsilon }_r\right)$ and relative permeability ($\left({\mathrm{\mu }}_{\mathrm{r}}\right)$ ). The refractive index is defined as $\sqrt{{\mathrm{\mu }}_{\mathrm{r}}{\mathrm{\epsilon }}_{\mathrm{r}}}=\mathrm{n}$.For ordinary material ${\mathrm{\epsilon }}_{\mathrm{r}}>0$ and ${\mathrm{\mu }}_{\mathrm{r}}>0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist $\mathrm{V}$. Veselago postulated the existence of material with ${\epsilon }_r<0$ and ${\mu }_r< 0$. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials $\mathrm{n}=-\sqrt{{\mathrm{\epsilon }}_{\mathrm{r}}{\mathrm{\mu }}_{\mathrm{r}} }$ . As light enters a medium of such refractive index the phases travel away from the direction of propagation.

According to the description above show that if rays of light enter such a medium from air (refractive index =$1$) at an angle$\theta$ in $2^{nd}$quadrant, them the refracted beam is in the $3^{rd}$quadrant.

The optical properties of a medium are governed by the relative permitivity $\left({\epsilon }_r\right)$ and relative permeability ($\left({\mathrm{\mu }}_{\mathrm{r}}\right)$ ). The refractive index is defined as $\sqrt{{\mathrm{\mu }}_{\mathrm{r}}{\mathrm{\epsilon }}_{\mathrm{r}}}=\mathrm{n}$.For ordinary material ${\mathrm{\epsilon }}_{\mathrm{r}}>0$ and ${\mathrm{\mu }}_{\mathrm{r}}>0$ and the positive sign is taken for the square root. In $1964$, a Russian scientist $\mathrm{V}$. Veselago postulated the existence of material with ${\epsilon }_r<0$ and $\mathrm{\mu r} < 0$. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials $\mathrm{n}=-\sqrt{{\mathrm{\epsilon }}_{\mathrm{r}}{\mathrm{\mu }}_{\mathrm{r}} }$ . As light enters a medium of such refractive index the phases travel away from the direction of propagation.

Prove that Snell’s law holds for such a medium.

To ensure almost $100$ per cent transmittivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is ${\mathrm{MgF}}_2 (\mathrm{n} = 1.38)$. What should the thickness of the film be so that at the center of the visible speetrum $\left(5500 \dot{\mathrm{A}}\right)$ there is maximum transmission.