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

The angles of incidence and refraction of a monochromatic ray of light of wavelength $\lambda$ at an air-glass interface are $i$ and $r$,respectively. $A$ parallel beam of light with a small spread $\delta \lambda$ in wavelength about a mean wavelength $\lambda$ is refracted at the same air-glass interface. The refractive index $\mu$ of glass depends on the wavelength $\lambda$ as $\mu(\lambda)=a+b / \lambda^2$,where $a$ and $b$ are constants. Then,the angular spread in the angle of refraction of the beam is

The frequency of a light ray is $6 \times 10^{14} \,Hz$. Its frequency when it propagates in a medium of refractive index $1.5$, will be

$A$ ray of light travelling in a medium of refractive index $\mu$ is incident at an angle $\theta$ on a composite transparent plate consisting of $50$ plates of refractive indices $1.01\mu, 1.02\mu, 1.03\mu, \dots, 1.50\mu$. The ray emerges from the composite plate into a medium of refractive index $1.6\mu$ at an angle $x$. Then:

$A$ light beam is travelling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I$,$II$,$III$,and $IV$ are $n_0$,$\frac{n_0}{2}$,$\frac{n_0}{6}$,and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is:

The refractive index of air is $1.0003$. The thickness of an air column that will contain one more wavelength of yellow light $(6000 \mathring A)$ than in the same thickness in a vacuum is: