The slits in a Young's double-slit experiment have equal widths, and the source is placed symmetrically relative to the slits. The intensity at the central fringe is $I_0$. If one of the slits is closed, the intensity at this point will be

At two points $P$ and $Q$ on the screen in Young's double-slit experiment,waves from slits $S_1$ and $S_2$ have a path difference of $0$ and $\frac{\lambda}{4}$ respectively. The ratio of intensities at $P$ and $Q$ will be

In Young's double-slit experiment,using light of wavelength $\lambda = 5890 \ \mathring{A}$,the angular width of the fringe is $0.20^\circ$. To increase the angular width by $10\%$,the wavelength must be increased by .......... $\mathring{A}$.

In a Young's double-slit experiment,the wavelength of light used is $6000 \, \mathring A$. The phase difference between the central bright fringe and the third bright fringe is .......

In a $YDSE$ apparatus,two identical slits are separated by $1\, mm$ and the distance between the slits and the screen is $1\, m$. The wavelength of light used is $6000\, \mathring{A}$. The minimum distance between two points on the screen having $75\%$ intensity of the maximum intensity is ......$mm$.

In the double slit experiment,when a glass plate (refractive index $\mu = 1.5$) of thickness $t$ is introduced in the path of one of the interfering beams (wavelength $\lambda$),the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is