In a vessel of $21 \, cm$ depth,up to what height should water be filled so that it appears to be $20\%$ filled when viewed from the top (in $, cm$)? (Given: $\mu_{water} = 4/3$)

$A$ concave mirror is placed over a beaker containing water of refractive index $\mu = 1.33$. The object is placed at the bottom of the beaker. If the image of the object is formed at a distance of $25 \, cm$ from the top surface of the water,and the mirror is at a height of $15 \, cm$ above the water surface,find the focal length of the mirror in $cm$.

$A$ glass slab of thickness $4 \ cm$ contains the same number of waves as $5 \ cm$ of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $4/3$. What is the refractive index of glass?

$A$ beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from

An air bubble in a glass slab of thickness $15 \, cm$ appears to be at $6 \, cm$ from one side and at $4 \, cm$ from the opposite side. The refractive index of the glass is:

$A$ ball is dropped from a height of $20 \,m$ above the surface of water in a lake. The refractive index of water is $4/3$. $A$ fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \,m$ above the water surface, the fish sees the speed of the ball as (Take $g = 10 \,m/s^2$): (in $\,m/s$)