The direction of the first secondary maximum in the Fraunhofer diffraction pattern at a single slit is given by:
\((a\) is the width of the slit) 
1. \(a\sin\theta = \frac{\lambda}{2}\)
2. \(a\cos\theta = \frac{3\lambda}{2}\)
3. \(a\sin\theta = \lambda\)
4. \(a\sin\theta = \frac{3\lambda}{2}\)

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the edges of the slit is:
1. \(0\)
2. \(\dfrac \pi 2 \)
3. \(\pi\)
4. \(2\pi\)

A parallel beam of monochromatic light of wavelength \(5000~\mathring{A}\) is incident normally on a single narrow slit of width \(0.001\) mm. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to:
1. \(0^{\circ}\)
2. \(15^{\circ}\)
3. \(30^{\circ}\)
4. \(60^{\circ}\)

In the far field diffraction pattern of a single slit under polychromatic illumination, the first minimum with the wavelength ${\lambda }_1$ is found to be coincident with the third maximum at ${\lambda }_2$. So

(1) $3{\lambda }_1=0.3{\lambda }_2$

(2) $3{\lambda }_1={\lambda }_2$

(3) ${\lambda }_1=3.5{\lambda }_2$

(4) $0.3{\lambda }_1=3{\lambda }_2$

The angle of polarisation for any medium is \(60^\circ,\) what will be the critical angle for this?

A beam of light AO is incident on a glass slab (μ = 1.54) in a direction as shown in figure. The reflected ray OB is passed through a Nicol prism on viewing through a Nicole prism, we find on rotating the prism that, 

1. the intensity is reduced down to zero and remains zero.
2. the intensity reduces down some what and rises again.
3. there is no change in intensity.
4. the intensity gradually reduces to zero and then again increases.

In the propagation of electromagnetic waves, the angle between the direction of propagation and plane of polarisation is:

(1) 0^o

(2) 45^o

(3) 90^o

(4) 180^o

An unpolarised light incident on a polariser has amplitude \(A\), and the angle between analyzer and polariser is \(60^{\circ}\). The light transmitted by the analyzer has an amplitude of:
1. \(A\sqrt{2}\)
2. \(\frac{A}{2\sqrt{2}}\)
3. \(\frac{\sqrt{3}A}{2}\)
4. \(\frac{A}{2}\)

Light passes successively through two polarimeters tubes each of length 0.29m. The first tube contains dextro rotatory solution of concentration 60kgm^–3 and specific rotation 0.01rad m²kg^–1. The second tube contains laevo rotatory solution of concentration 30kg/m³ and specific rotation 0.02 radm²kg^–1. The net rotation produced is 

(1) 15°

(2) 0°

(3) 20°

(4) 10°

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam?

$Given:$
$\cos {75}^0 =0.26$
$\cos {57}^0 =0.57$
$\cos {35}^0 =0.82$
$\cos {15}^0 =0.96$
$$

(1) 75°

(2) 55°

(3) 35°

(4) 15°