For a colour of light,the wavelength in air is $6000 \ \mathring A$ and in water,the wavelength is $4500 \ \mathring A$. Then the speed of light in water will be:

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 $\text{cm}$.

$A$ ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with angle of incidence $i$ in medium $X$ and angle of refraction $r$ in medium $Y$. The given graph shows the relation between $\sin i$ and $\sin r$. If $V_X$ and $V_Y$ are the velocities of the ray in media $X$ and $Y$ respectively, then which of the following is true?

$A$ wave has velocity $u$ in medium $P$ and velocity $2u$ in medium $Q.$ If the wave is incident in medium $P$ at an angle of $30^\circ,$ then the angle of refraction will be .... $^o$

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

$A$ beam of light propagating in medium $A$ with index of refraction $n(A)$ passes across an interface into medium $B$ with index of refraction $n(B)$. The angle of incidence is greater than the angle of refraction; $v(A)$ and $v(B)$ denote the speed of light in $A$ and $B$. Then which of the following is true?