In a Young's double slit experiment, the slit separation is 1.5 mm . The setup is illuminated simultaneously by light of wavelengths $6000 \mathop {\rm{A}}\limits^{\rm{o}}$ and $8000 \mathop {\rm{A}}\limits^{\rm{o}}$. The screen is placed at a distance of 1.5 m from the slits. It is observed that at a certain point $P$ on the screen which is 4.8 mm from the central maximum, fringes due to both the wavelengths coincide.

Which of the following options are correct?

A. Light of wavelength $6000\mathop {\rm{A}}\limits^{\rm{o}}$ produces a dark fringe and light of wavelength $8000 \mathop {\rm{A}}\limits^{\rm{o}}$ produces a bright fringe at P

B. Light of wavelength $6000 \mathop {\rm{A}}\limits^{\rm{o}}$ produces a bright fringe and light of wavelength $8000 \mathop {\rm{A}}\limits^{\rm{o}}$ produces a dark fringe at P

C. Light of wavelength $6000\mathop {\rm{A}}\limits^{\rm{o}}$ and light of wavelength $8000 \mathop {\rm{A}}\limits^{\rm{o}}$ both produce a dark fringe at P

D. Light of wavelength $6000 \mathop {\rm{A}}\limits^{\rm{o}}$ and light of wavelength $8000\mathop {\rm{A}}\limits^{\rm{o}}$ both produce a bright fringe at P

In a Young's double slit experiment, the slits are separated by 0.5 mm . Fringes are obtained on a screen which is placed at distance 1 m away from the slits. When the screen is moved 7 cm farther away, the fringe width changes by $63 \mu \mathrm{~m}$. The wavelength of light used in the experiment will be:

The interference pattern is obtained with two coherent light sources of intensity ratio $9: 1$. The ratio of $\frac{I_{\operatorname{MAX}}+I_{\operatorname{MIN}}}{I_{\operatorname{MAX}}-I_{\operatorname{MIN}}}$ is $\frac{\alpha}{\beta}$. The values of $\alpha$ and $\beta$ are:

The wavelength of a monochromatic light which is used in single slit diffraction is 800 nm . The width of the single slit for which the first minimum appears at $\theta=45^{\circ}$ on the screen will be: