The frequency of a light wave in a material is $2 \times 10^{14} \mathrm{~Hz}$ and wavelength is $5000 \mathop {\rm{A}}\limits^{\rm{o}} $. The refractive index of material will be

A thin plano-convex lens of focal length $f$ is split into two halves one of the halves is shifted along the optical axis. The separation between object and image formed by one of the half-lenses is 2.4 and the magnification of same lens is 2. If $f$ and $d$ be the focal length of the lens and separation between the two halves respectively then

A vessel is half filled with a liquid of refractive index $\mu$. The other half of the vessel is filled with an immiscible liquid of refractive index $2 \mu$. The apparent depth of the vessel is $50 \%$ of the actual depth. Then $\mu$ is

A mosquito O is sitting infront of a glass rod having spherical end of radius of curvature 40 cm. The image would be formed at

An achromatic convergent doublet of two lenses in contact has a power of +5 D. The power of converging lens is +6 D. The ratio of the dispersive power of the convergent and divergent lenses is

The property of light used in optical fibre cables is

Two plane mirrors A and B are aligned parallel to each other as shown in the figure.

A ray of light is incident at an angle 30$^\circ$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times, the ray undergoes reflection (excluding the first one) before it emerges out is

A thin equi-convex lens is made of glass of refractive index 1.5 and its focal length is 0.2 m. If it acts as a concave lens of focal length 0.5 cm when dipped in a liquid, the refractive index of the liquid is

A spherical lens of power $-$4D is placed at a distance of 15 cm from another spherical lens of power 5 D. A beam of parallel light falls on the first spherical lens. The final image formed is