In Young's double-slit experiment, the separation between the slits is 0.5 mm. Source of light S is placed at a distance of 0.5 mm from the slit $S_1$ as shown in the figure. To have central maxima at mid-point O, the glass plate of refractive index 1.5 is placed in front of $S_1$. The thickness of the plate is:

                    

1.  ($\sqrt{2}$ - 1) mm

2.  ($\sqrt{2}$ + 1) mm

3.  $\sqrt{2}$ mm

4.  $\frac{1}{\sqrt{2}}$ mm

 

If the \(5\)th order maxima of wavelength \(4000~\mathring{A}\) in Young's double-slit experiment coincides with the \(n\)th order maxima of wavelength \(5000~\mathring{A},\) then \(n\) is equal to:
1. \(5\)
2. \(8\)
3. \(4\)
4. \(10\)

Light of wavelength 6000 $\stackrel{\mathrm{o}}{\mathrm{A}}$ in air enters a medium of refractive index 1.5. Frequency and wavelength of light in the medium respectively are 

1.  $5 \times {10}^{14} \mathrm{Hz}, 6000 \stackrel{\mathrm{o}}{\mathrm{A}}$

2.  $5 \times {10}^{14} \mathrm{Hz}, 4000 \stackrel{\mathrm{o}}{\mathrm{A}}$

3.  $\frac{10}{3} \times {10}^{14} \mathrm{Hz}, 4000 \stackrel{\mathrm{o}}{\mathrm{A}}$

4.  $\frac{10}{3} \times {10}^{14} \mathrm{Hz}, 6000 \stackrel{\mathrm{o}}{\mathrm{A}}$

The ratio of angular width of principal maximum to the angular width of the secondary maximum in single slit diffraction is

1.  4 : 1

2.  2 : 1

3.  5 : 1

4.  3 : 1

The resolving power of a microscope can be increased by using:

1.  red light.
2.  blue light.
3.  oil between objective lens and object.
4.  both (2) and (3).

Monochromatic light of a wavelength $\lambda$ in air is refracted into a glass slab of refractive index $\mu$. The wavelength of light in the glass is

1.  $\lambda$

2.  $\mu$$\lambda$

3.  $\frac{\lambda }{\mu }$

4.  $\frac{\lambda }{{\mu }^2}$

Two coherent sources are 0.3 mm apart. They are 1 m away from the screen. The second dark fringe is at a distance of 0.3 cm from the center. The distance of the fourth bright from the centre is

1.  0.16 cm

2.  1.6 cm

3.  0.8 cm

4.  8 cm

Assume that light of wavelength 7000 $\stackrel{\mathrm{o}}{\mathrm{A}}$ is coming from a star. The limit of resolution (in radian) of a telescope whose objective has a diameter of 244 cm, will be

1.  $2.5 \times {10}^{-7}$

2.  $5.0 \times {10}^{-7}$

3.  $3.5 \times {10}^{-7}$

4.  $4.5 \times {10}^{-7}$

Light of wavelength 5000 $\stackrel{\mathrm{o}}{\mathrm{A}}$ travelling at a speed of $2 \times {10}^8$m/s in medium 1 is incident on a boundary and gets refracted into medium 2. Its wavelength after refraction is found to be 5500 $\stackrel{\mathrm{o}}{\mathrm{A}}$. Which of the following is incorrect?

1.  Refractive index of medium 2 is $\frac{11}{10}$.

2.  On entering medium 2, light bends away from normal.

3.  Speed of light is more in medium 2 than in medium 1.

4.  Its frequency remains unchanged.

Yellow light is used in a single slit diffraction pattern with a slit width of 0.5 mm. If the yellow light is replaced by X-rays, then the observed pattern will reveal

1.  No diffraction pattern

2.  More narrow central maximum

3.  More number of fringes

4.  Less number of fringes