The basic reason for the extraordinary sparkle of suitably cut diamond is thatit has a very high refractive index.

Optical fiber works on the principle of total internal reflection.

The Total Internal Reflection is the phenomenon in which the complete reflection of a light ray reaching an interface with a less dense medium when the angle of incidence exceeds the critical angle.

Force and Pressurephysical quantities do not have same dimensions.

When body is accelerated thanits speed may or maynot change.

Because the elastic force is a conservative force, we can use the Work-Energy Theorem and Conservation of Energy to write the following equation:

E = K+U =$\frac{1}{2}m{v}^2$+$\frac{1}{2}k{x}^2$

For conservative forces, E = 0, and the equation simplifies to K = U:

$\frac{1}{2}m{v}^2=\frac{1}{2}k{v}^2$

Substitute x for the initial displacement of A, and solve for velocity v:

$\frac{1}{2}m{v}^2=\frac{1}{2}k{A}^2$

⇒$v^2=\frac{k{A}^2}{m}$

⇒ v = A$\sqrt{\frac{k}{m}}$

A periscope is an optical instrument that uses a system of prisms, lenses, or mirrors to reflect images through a tube.

Light from a distant object strikes the top mirror and is then reflected at an angle of 90 degrees down the periscope tube. At the bottom of the periscope, the light strikes another mirror and is then reflected into the viewer’s eye.

Hence, A periscope works by the principle of Total internal reflection.

The lens which have atleast one inward curved surface is a concave lens. Concave ens is a diverging lens as it spreads out light rays that have been refracted through it.

A concave lens is thinner at its centre than at its edges.

In series : E1 + E2 = K(50)

In parallel : E1 - E2 = K(10)

E1 + E2 / E1 - E2 = 5/1

=> E1/E2 = 3/2

The emf's are in the ratio of 3:2.

Heat always flows from a body at higher temperature to a body at a lower temperature.

At the time of jumping out he has the same velocity as the moving train.