The ratio of intensities of two points on a screen in Young's double slit experiment when waves from the two slits have a path difference of $$\frac{\lambda}{4}$$ and $$\frac{\lambda}{6}$$ is

$$\left(\cos 90^{\circ}=0, \cos 60^{\circ}=0.5\right)$$

In Young's double slit experiment 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

One of the slits in Young's double slit experiment is covered with a transparent sheet of thickness $$2.9 \times 10^{-3} \mathrm{~cm}$$. The central fringe shifts to a position originally occupied by the $$25^{\text {th }}$$ bright fringe. If $$\lambda=5800$$ $$\mathop A\limits^o $$, the refractive index of the sheet is

In Young's double slit experiment the intensities at two points, for the path difference $$\frac{\lambda}{4}$$ and $$\frac{\lambda}{3}$$ ($$\lambda=$$ wavelength of light used) are $$I_1$$ and $$I_2$$ respectively. If $$\mathrm{I}_0$$ denotes the intensity produced by each one of the individual slits then $$\frac{\mathrm{I}_1+\mathrm{I}_2}{\mathrm{I}_0}$$ is equal to $$\left(\cos 60^{\circ}=0.5, \cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$