If $$\hat{n}_1, \hat{n}_2$$ and $$\hat{\mathrm{t}}$$ represent, unit vectors along the incident ray, reflected ray and normal to the surface respectively, then

When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is 45 cm from the lens is formed 36 cm above the lens. When a liquid is poured in the tank to a depth of 40 cm, the distance of the image of the mark above the lens is 48 cm. The refractive index of the liquid is

Three identical convex lenses each of focal length $$\mathrm{f}$$ are placed in a straight line separated by a distance $$\mathrm{f}$$ from each other. An object is located at f/2 in front of the leftmost lens. Then,

The human eye has an approximate angular resolution of $$\theta$$ = 5.8 $$\times$$ 10^{$$-$$4} rad and typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance d should a printed page be held so that one does not see the individual dots?