The frequency of a light wave in a material is $2 \times 10^{14} \ Hz$ and its wavelength is $5000 \ \mathring{A}$. The refractive index of the material will be:

Green light of wavelength $5460 \mathring{A}$ is incident on an air-glass interface. If the refractive index of glass is $1.5$,the wavelength of light in glass would be ........ $\mathring{A}$.

Light of wavelength $300 \ nm$ in medium $A$ enters into medium $B$ through a plane surface. If the frequency of light is $5 \times 10^{14} \ Hz$ and the ratio of speed in medium $A$ to that in medium $B$ is $\frac{4}{5}$,the absolute refractive index of medium $B$ is:

Light enters from air into a given medium at an angle of $45^{\circ}$ with the interface of the air-medium surface. After refraction,the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is

If light passes near a massive object,the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by $n = 1 + \frac{2GM}{rc^2}$,where $r$ is the distance of the point of consideration from the centre of the mass of the massive body,$G$ is the universal gravitational constant,$M$ is the mass of the body,and $c$ is the speed of light in vacuum. Considering a spherical object,find the deviation of the ray from the original path as it grazes the object.

$A$ ray of light passes through four transparent media with refractive indices $n_{1}$,$n_{2}$,$n_{3}$,and $n_{4}$ as shown. The surfaces of all media are parallel. If the emergent ray $DE$ is parallel to the incident ray $AB$,then