$A$ 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

Two light beams fall on a transparent material block at points $1$ and $2$ with angles $\theta_1$ and $\theta_2$ respectively,as shown in the figure. After refraction,the beams intersect at point $3$,which is exactly on the interface at the other end of the block. Given: the distance between $1$ and $2$ is $d = 4\sqrt{3} \text{ cm}$ and $\theta_1 = \theta_2 = \cos^{-1}\left(\frac{n_2}{2n_1}\right)$,where $n_2$ is the refractive index of the block and $n_1$ is the refractive index of the outside medium $(n_2 > n_1)$. Find the thickness of the block in $\text{cm}$.

$A$ monochromatic beam of light passes from a denser medium into a rarer medium. As a result,

$A$ beam of light is incident on a glass plate at an angle of $60^{\circ}$. The reflected ray is polarized. If the angle of incidence is $45^{\circ}$,then the angle of refraction is:

If the wavelength of light in air is $4200\, \mathring A$,what will be the wavelength of light in water $(\mu = 4/3)$ in $\mathring A$?

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