Two polaroids \(P_{1}\) and \(P_{2}\) are placed with their axis perpendicular to each other. Unpolarised light \(I_{o}\) is incident on \(P_{1}\). A third polaroid \(P_{3}\) is kept in between  \(P_{1}\) and \(P_{2}\)  such that its axis makes an angle \(\left(45\right)^{\circ}\) with that of \(P_{1}\). The intensity of transmitted light through \(P_{2}\)

1. \(\frac{I_{o}}{2}\)

2. \(\frac{I_{o}}{4}\)

3. \(\frac{I_{o}}{8}\)

4. \(\frac{I_{o}}{16}\)

$\frac{\mathrm{}}{}$

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be

1.$\frac{\sqrt{n}}{n+1}$             

2. $\frac{2\sqrt{n}}{n+1}$

3. $\frac{\sqrt{n}}{{\left(n+1\right)}^2}$         

4.$\frac{2\sqrt{n}}{{\left(n+1\right)}^2}$

A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength $5\times {10}^{-5}$ cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is

(1) 0.10 cm             

(2) 0.25 cm 

(3) 0.20 cm             

(4) 0.15 cm

The intensity at the maximum in Young's double-slit experiment is ${\mathrm{I}}_0$ when the distance between two slits is d=5$\lambda$, where $\lambda$ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance D= 10 d?

(1) $\frac{{\mathrm{I}}_0}{4}$               

(2) $\frac{3}{4}{\mathrm{I}}_0$

(3) $\frac{{\mathrm{I}}_0}{2}$             

(4) ${\mathrm{I}}_0$

In a diffraction pattern due to a single slit of width a,the first minimum is observed at an angle ${30}^{\circ }$ when light of wavelength 5000 $\dot{A}$ is incident on the slit. The first secondary maximum is observed at an angle of 

(a) ${\sin }^{-1}\left(\frac{2}{3}\right)$           (b) ${\sin }^{-1}\left(\frac{1}{2}\right)$

(c) ${\sin }^{-1}\left(\frac{3}{4}\right)$           (d) ${\sin }^{-1}\left(\frac{1}{4}\right)$

For a parallel beam of monochromatic light of wavelength diffraction is produced by a single slit whose width 'a' is of the order of the wavelength of the light. If 'D' is the distance of the screen from the slit, the width of the central maxima will be

(1)2Dλ/a

(2)Dλ/a

(3)Da/λ

(4)2Da/λ

In a double-slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double-slit within the central maxima of a single-slit pattern?

1. 0.2 mm

2. 0.1 mm

3. 0.5 mm

4. 0.02 mm

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

(1) π/4 radian

(2) π/2 radian

(3) π radian

(4) π/8 radian

A beam of light of 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is
                      
1. 1.2cm

2. 1.2mm

3. 2.4cm

4. 2.4mm