An object is immersed in a fluid of refractive index $\mu$. In order that the object becomes invisible when observed from outside,it should

$A$ fish rising vertically up towards the surface of water with speed $3 \; ms^{-1}$ observes a bird diving vertically down towards it with speed $9 \; ms^{-1}$. The actual velocity of the bird is.......$ms^{-1}$ (Assume refractive index of water $\mu = 4/3$).

$A$ light beam is incident on a denser medium whose refractive index is $1.414$ at an angle of incidence $45^o$. Find the ratio of the width of the refracted beam in the medium to the width of the incident beam in air.

The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

In the figure below,$PQRS$ denotes the path followed by a ray of light as it travels through three media in succession. The absolute refractive indices of the media are $\mu_1, \mu_2$ and $\mu_3$,respectively. (The line segment $RS$ in the figure is parallel to $PQ$). Then,

$A$ 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 $n(z)$