JEE Main 2017 — Optics

In an experiment a convex lens of focal length $15\mathrm{cm}$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5\mathrm{cm}$ from it. It is found that an object and its image coincide, if the object is placed at a distance of $20\mathrm{cm}$ from the lens. The focal length of the convex mirror is-

In a Young's double slit experiment, slits are separated by $0.5\mathrm{mm}$, and the screen is placed $150\mathrm{cm}$ away. A beam of light consisting of two wavelengths, $650\mathrm{nm}$ and $520\mathrm{nm}$, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is:

A single slit of width $0.1\mathrm{mm}$ is illuminated by a parallel beam of light of wavelength $6000 Å$ and diffraction bands are observed on a screen $0.5m$ from the slit. The distance of the third dark band from the central bright band is:

A diverging lens with magnitude of focal length $25\mathrm{cm}$ is placed at a distance of $15\mathrm{cm}$ from a converging lens of magnitude of focal length $20\mathrm{cm}$. A beam of parallel light falls on the diverging lens. The final image formed is:

Let the refractive index of a denser medium with respect to rarer medium be ${n}_{12}$ and its critical angle be ${\theta }_{C}$ . At an angle of incidence $A$ when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is ${90}^{o}$. Angle $A$ is given by

A single slit of width $b$ is illuminated by a coherent monochromatic light of wavelength $\lambda .$ If the second and fourth minima in the diffraction pattern at a distance $1\mathrm{cm}$ from the slit are at $3\mathrm{cm}$ and $6\mathrm{cm}$ respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum)