Consider a ray of light incident from the 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:

$$\begin{gathered} \left(1\right) \frac{4\pi d}{\lambda }{\left(1-\frac{1}{n^2}{\sin }^2\theta \right)}^{-1/2}+\pi \\ \left(2\right) \frac{4\pi d}{\lambda }{\left(1-\frac{1}{n^2}{\sin }^2\theta \right)}^{-1/2} \\ \left(3\right) \frac{4\pi d}{\lambda }{\left(1-\frac{1}{n^2}{\sin }^2\theta \right)}^{-1/2}+\frac{\pi }{2} \\ \left(4\right)\hspace{0.17em}\frac{4\pi d}{\lambda }{\left(1-\frac{1}{n^2}{\sin }^2\theta \right)}^{-1/2}+2\pi \end{gathered}$$

In 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,

The figure shows a standard two-slit arrangement with slits ${\mathrm{S}}_1, {\mathrm{S}}_2. {\mathrm{P}}_1, {\mathrm{P}}_2$ are the two minima points on either side of P (figure).

At ${\mathrm{P}}_2$ on the screen, there is a hole and behind ${\mathrm{P}}_2$ is a second 2-slit arrangement with slits ${\mathrm{S}}_3, {\mathrm{S}}_4$ and a second screen behind them. 

Two Sources ${\mathrm{S}}_1 \mathrm{and} {\mathrm{S}}_2$ of intensity $I_1 and l_2$ are 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?

(a) $S_{1}and S_2$ have the same intensities
(b) $S_{1}and S_2$ have a constant phase difference
(c) $S_{1}and S_2$ have the same phase
(d) $S_{1}and S_2$ have the same wavelength 

Consider sunlight incident on a pinhole of width ${10}^3$ $\stackrel{\circ }{A}$. The image of the pinhole seen on a screen shall be:

(a) a sharp white ring
(b) different from a geometrical image
(c) a diffused central spot, white in colour
(d) diffused coloured region around a sharp central white spot

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

(a) the size decreases
(b) the intensity increases
(c) the size increases
(d) the intensity decreases

For light diverging from a point source,

(a) the wavefront is spherical
(b) the intensity decreases in proportion to the distance squared
(c) the wavefront is parabolic
(d) the intensity at the wavefront does not depend on the distance

Two coherent sources of light interfere and produce fringe pattern on a screen. For the central maximum, the phase difference between the two waves will be: 

What speed should a galaxy move with respect to us so that the sodium line at 589.0 nm is observed at 589.6 nm?

Which one of the following is incorrect?

Two slits are made one millimeter apart and the screen is placed one meter away. What is the fringe separation when blue-green light of wavelength 500 nm is used? 

Assume that light of wavelength 6000Å is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 100 inches?

$$\begin{gathered} 1. 1.2\times {10}^{-6} \mathrm{radians} \\ 2. 3.3\times {10}^{-7} \mathrm{radians} \\ 3. 1.7\times {10}^{-6} \mathrm{radians} \\ 4. 2.9\times {10}^{-7} \mathrm{radians} \end{gathered}$$

For what distance is ray optics a good approximation when the aperture is 3 mm wide and the wavelength is 500 nm?

The expression for intensity (as shown in the figure) of transmitted light when a polaroid sheet is rotated between two crossed polaroids is:

[Given: I_o is the intensity of transmitted light from polariser A]

$$\begin{gathered} 1. \mathrm{I}=\frac{{\mathrm{I}}_0}{2}{\sin }^{2}2\mathrm{\theta } \\ 2. \mathrm{I}=\frac{{\mathrm{I}}_0}{4}{\sin }^{2}2\mathrm{\theta } \\ 3. \mathrm{I}=\frac{{\mathrm{I}}_0}{2}{\cos }^{2}2\mathrm{\theta } \\ 4. \mathrm{I}=\frac{{\mathrm{I}}_0}{4}{\cos }^{2}2\mathrm{\theta } \end{gathered}$$

Unpolarised light is incident on a plane glass surface. What should be the angle of incidence so that the reflected and refracted rays are perpendicular to each other?

$$\begin{gathered} 1. {45}^0 \\ 2. {67}^0 \\ 3. {57}^0 \\ 4. {37}^0 \end{gathered}$$

Consider the following statements and then mark the incorrect statement/s.

(a) The angular separation of the fringes increases if the screen is moved towards the plane of the slits.

(b) The angular separation of the fringes increases if the (monochromatic) source is replaced by another (monochromatic) source of a shorter wavelength.

(c) The angular separation of the fringes increases if the separation between the two slits is increased.

(d) The sharpness of the fringes increases when the source slit is moved closer to the double-slit plane.

Two slits are made one millimetre apart and the screen is placed one metre away. What should the width of each slit be to obtain 10 maxima of the double-slit pattern within the central maximum of the single slit pattern?