Consider a light beam incident from air to a glass slab at Brewster's angle as shown in figure.

A polaroid is placed in the path of the emergent ray at point $P$ and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid.

Consider sunlight incident on a slit of width $10^4 \mathop A\limits^o$. The image seen through the slit shall

Consider a ray of light incident from air onto a slab of glass (refractive index $n$ ) of width $d$, at an angle $\theta$. The phase difference between the ray reflected by the top surface of the glass and the bottom surface is

In a Young's double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case,

Figure shows a standard two slit arrangement with slits $S_1, S_2, P_1, P_2$ are the two minima points on either side of $P$ (figure).

At $P_2$ on the screen, there is a hole and behind $P_2$ is a second 2-slit arrangement with slits $S_3, S_4$ and a second screen behind them.

Two sources $S_1$ and $S_2$ of intensity $I_1$ and $I_2$ are placed in front of a screen [Fig. (a)]. The pattern of intensity distribution seen in the central portion is given by Fig. (b).

In this case, which of the following statements are true?

Consider sunlight incident on a pinhole of width $10^3 \mathop A\limits^o$. The image of the pinhole seen on a screen shall be

Consider the diffraction pattern for a small pinhole. As the size of the hole is increased

For light diverging from a point source,

Is Huygen's principle valid for longitudinal sound waves?

Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is the nature of the wavefronts emerging from the final image?

What is the shape of the wavefront on earth for sunlight?

Why is the diffraction of sound waves more evident in daily experience than that of light wave?

The human eye has an approximate angular resolution of $\phi=5.8 \times 10^{-4}$ rad and a typical photoprinter prints a minimum of 300 dpi (dots per inch, 1 inch $=2.54 \mathrm{~cm}$ ). At what minimal distance $z$ should a printed page be held so that one does not see the individual dots.

A polaroid (I) is placed infront of a monochromatic source. Another polariod (II) is placed in front of this polaroid (I) and rotated till no light passes. A third polaroid (III) is now placed in between (I) and (II). In this case, will light emerge from (II). Explain.

Can reflection result in plane polarised light if the light is incident on the interface from the side with higher refractive index?

'For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of $5000 \mathop A\limits^o$ and electrons accelerated through 100 V used as the illuminating substance.

Consider a two slit interference arrangements (figure) such that the distance of the screen from the slits is half the distance between the slits. Obtain the value of $D$ in terms of $\lambda$ such that the first minima on the screen falls at a distance $D$ from the centre 0.

Figure shown a two slit arrangement with a source which emits unpolarised light. $P$ 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.

$$A C=C O=D, S_1 C=S_2 C=d \ll D$$

A small transparent slab containing material of $\alpha=1.5$ is placed along $A S_2$ (figure). What will be the distance from 0 of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab?

Four identical monochromatic sources $A, B, C, D$ as shown in the (figure) produce waves of the same wavelength $\lambda$ and are coherent. Two receiver $R_1$ and $R_2$ are at great but equal distances from $B$.

(i) Which of the two receivers picks up the larger signal?

(ii) Which of the two receivers picks up the larger signal when $B$ is turned off?

(iii) Which of the two receivers picks up the larger signal when $D$ is turned off?

(iv) Which of the two receivers can distinguish which of the sources $B$ or $D$ has been turned off?

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

(i) 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, then the refracted beam is in the 3rd quadrant.

(ii) Prove that Snell's law holds for such a medium.

To ensure almost $100 \%$ 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 $\mathrm{MgF}_2(n=1.38)$. What should the thickness of the film be so that at the centre of the visible spectrum ( $5500 \mathop A\limits^o$ ) there is maximum transmission.