In the Young's double-slit experiment, the spacing between two slits is $0.1 \, mm$. If the screen is kept at a distance of $1.0 \, m$ from the slits and the wavelength of light is $5000 \, \mathring{A}$, then the fringe width is ........ $cm$.

White light is used to illuminate two slits in Young's double-slit experiment. The separation between the slits is $b$ and the screen is at a distance $d (d >> b)$ from the slits. The wavelengths missing at a point on the screen directly in front of one of the slits are

Given below are two statements:
Statement $I$: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits.
Statement $II$: In a Young's double slit experiment, the angular separation of fringes will increase when a monochromatic source is replaced by another monochromatic source of higher wavelength.
In the light of the above statements, choose the correct answer from the options given below:

Consider the following statements in the case of Young's double-slit experiment:
$(1)$ $A$ slit is necessary if we use an ordinary extended source of light.
$(2)$ $A$ slit is not necessary if we use an ordinary but well-collimated beam of light.
$(3)$ $A$ slit is not needed if we use a spatially coherent point source of light.
Which of the above statements is true?

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 .......... $\mathring{A}$.

Two thin parallel slits are made in an opaque screen. When a monochromatic beam of light passes through them at normal incidence,the first bright fringe in the transmitted light occurs at $\pm 45^{\circ}$ with the original direction of the light beam on a distant screen when the apparatus is in air. When the apparatus is immersed in a liquid,the same bright fringe now occurs at $\pm 30^{\circ}$. The refractive index of the liquid is: