The diffraction fringes obtained by a single slit are of

In Young's double slit experiment, $$8^{\text {th }}$$ maximum with wavelength '$$\lambda_1$$' is at a distance '$$d_1$$' from the central maximum and $$6^{\text {th }}$$ maximum with wavelength '$$\lambda_2$$' is at a distance '$$\mathrm{d}_2$$'. Then $$\frac{\mathrm{d}_2}{\mathrm{~d}_1}$$ is

If $$\mathrm{I}_0$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be the intensity when the slit width is doubled?

Light of wavelength $$5000 \mathop A\limits^o$$ is incident normally on a slit. The first minimum of the diffraction pattern is observed to lie at a distance of $$5 \mathrm{~mm}$$ from the central maximum on a screen placed at a distance of $$2 \mathrm{~m}$$ from the slit. The width of the slit is