An object at the bottom of a tank containing two different liquids (which do not mix with each other) is seen vertically from above . Prove the apparent depth pf the object is `frac(d_1)(mu_1)+frac(d_2)(mu_2)` if the lower and upper liquids are respectively of depths `d_1` and `d_2` and R.I. `mu_1` and `mu_2`.

A tank's depth is 2d and the apparent depth of the liquid in the tank is 60 % its actual depth. What is the refractive index of the liquid with respect to air?

Speed of light through two media of refractive indices mu_(1) and mu_(2) are u_(1) and u_(2) respectively, then

If f_1(x) and f_2(x) are defined on domains D_1 and D_2 ,respectively, then f_1 (x) + f_2(x) is defined on D_1 nn D_2 .

An object weighs m_1 in a liquid of density d_1 and that in liquid of density d_2 " is " m_2 . The density d of the object is

An object is placed at a certain depth from the upper surface of a liquid. When it is seen from air, it appears that the object is raised through (1)/(3) of the depth. Again if water is taken instead of the liquid it appears that the object is raised above through (1)/(4) of the real depth. Refractive index of liquid = (3)/(2) and refractive index of water = (4)/(3) . Explain the matter.

Prove that the points A(-2,-1) B(1,0), C(4,3) and D(1,2) are the vertices of a parallelogram. Is it a rectangle ?

Differentiate x^2+\ 1 with respect to x .