An observer can see the top of a thin rod of height $h$ through a pinhole. The height of the container is $3h$ and its radius is $2h$. When the container is filled with a liquid up to a height of $2h$,the observer can see the bottom end of the rod. Find the refractive index of the liquid.

The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of:

$A$ transparent slab of thickness $d$ has a refractive index $n(z)$ that increases with $z$. Here $z$ is the vertical distance inside the slab,measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2 (> n_1)$,as shown in the figure. $A$ ray of light is incident with angle $\theta_i$ from medium $1$ and emerges in medium $2$ with refraction angle $\theta_f$ with a lateral displacement $l$. Which of the following statement$(s)$ is(are) true?
$(A)$ $n_1 \sin \theta_i = n_2 \sin \theta_f$
$(B)$ $n_1 \sin \theta_i = (n_2 - n_1) \sin \theta_f$
$(C)$ $l$ is independent of $n_2$
$(D)$ $l$ is dependent on $n(z)$

Assertion $(A)$: The colour of radiation does not change on passing through different media.
Reason $(R)$: The media do not absorb or emit colours.

The ratio of the refractive index of red light to blue light in air is

The velocity of light in glass,whose refractive index with respect to air is $1.5$,is $2 \times 10^8 \ m/s$. In a certain liquid,the velocity of light is found to be $2.5 \times 10^8 \ m/s$. The refractive index of the liquid with respect to air is: