In an optical instrument- microscope, the wavelength of light used are $\lambda_1 = 6800$ Å and $\lambda_2 = 5100$ Å. The ratio of the resolving power of microscope corresponding to '$\lambda_1$' to that for '$\lambda_2$' is

When a glass plate of refractive index $1.44$ is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$y$'. If this plate is replaced by another plate of same thickness but of refractive index $1.66$, the fringes will be displaced by a distance

In a certain region of the screen, number of fringes formed is observed to be 8 in Young's double slit experiment when light of wavelength $6600\ \text{Å}$ is used. If the light of wavelength $4400\ \text{Å}$ is used, the number of fringes observed in the same region of the screen will be

In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength $6480\ \text{Å}$, angular width of central maximum is measured. When the slit is illuminated by light of another wavelength '$\lambda$' the angular width decreases by $25\%$. The value of $\lambda$ in $\text{Å}$ units is