The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1$=4000 $\stackrel{0}{A}$ and ${\lambda }_2=6000 \stackrel{0}{A}$ is:-

1. 9:4

2. 3:2

3. 16:81

4. 8:27

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light of intensity I_o is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45° with that of P₁. The intensity of transmitted light through P₂ is:

1. $\frac{I_0}{4}$

2. $\frac{I_0}{8}$

3. $\frac{I_0}{16}$

4. $\frac{I_0}{2}$

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 x 10^-5 cm. The distance of the first dark band of the diffraction pattern from the center of the screen is:

1.  0.10 cm

2.  0.25 cm

3.  0.20 cm

4.  0.15 cm

In Young's double-slit experiment, the separation d between the slits is 2 mm, the wavelength $\lambda$ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same $\lambda$ and D) the separation between the slits needs to be changed to:

1. 1.8 mm

2. 1.9 mm

3. 2.1 mm

4. 1.7 mm

An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:

The intensity at the maximum in a Young's double-slit experiment is I₀. 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 = 10d?

1. $\frac{I_0}{4}$

2. $\frac{3}{4}{I}_0$

3. $\frac{I_0}{2}$

4. $I_0$

Two slits in young’s experiment have widths in the ratio 1:25. The ratio of intensity at the maxima and minima in the interference pattern $\frac{I_{max}}{I_{min}}$is

1. $\frac{9}{4}$

2. $\frac{121}{49}$

3. $\frac{49}{121}$

4. $\frac{4}{9}$

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. \(\frac{\pi}{4}~radian\)

2. \(\frac{\pi}{2}~radian\)

3. \(\pi~radian\)

4. \(\frac{\pi}{8}~radian\)$$