Examples Based on Newton's Laws of motion.

An army vehicle of mass 1000 kg is moving with a velocity of 10 m/s and is acted upon by a forward force of 1000 N due to the engine and a regarding force of 500 N due to friction. What will be it's velocity after 10 sec? 

Solution 

Examples related to Bowl Problem

Example on Conical Pendulum

Example based on Time Period and Frequency of Conical Pendulum.

Example based on Radius of Circular path of Conical Pendulum

Find Angular Frequency? Motion In plane (Vertical Circular Motion)

Question

A body of mass 5 kg is suspended by a spring balance on an inclined plane as shown in figure. The spring balance measures______

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Solution

Bowl Problem | Motion In plane |

Question 

Find the height from the centre of bowl, the block of mass 1kg leaves from bowl surface. What is the  speed of block at this instant. [ friction between bowl and block is o] R= 9m ; g = 10 m/s² .

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A block is kept at the top of the hemispherical bowl, fricition between the block and bowl is zero so block slides down. Find the angle and velocity of block at which block leaves the surface of bowl? 

Wave Optics

 Wave Optics -:

• Wave optics describes the relation between waves and rays of light.
•  According to wave theory of light, the light is a form of energy which travels through a medium in the form of wave motion. 
• The speed of light in a medium depends upon the nature of medium.
• Wave Optics also known as Physical Optics.
• It is based on the wave theory of light, which was first proposed by Dutch physicist Christiaan Huygens in 1678.
•  Wave optics is used to study the propagation of light, and to understand how it interacts with matter.

Wave Optics Theories

1. Theory of diffraction

2. Maxwell Electromagnetic Theory

3. Fresnel equations

4. Huygens’ principle

5. Theory of interference

Theory of diffraction

The theory of diffraction is used to explain the behavior of light when it hits to an obstacle. When light waves hits to an obstacle, they are scattered in all directions. The amount of scattering depends on the size and shape of the obstacle. This Scattering of light is a kind of Diffraction.

Theory of interference

The theory of interference is used to explain the behaviour of light when it encounters two or more obstacles. When light waves encounter two or more obstacles, they interact with each other and create a pattern of light and dark regions.

Huygens’ principle

Huygens’ principle is used to explain the behavior of light when it encounters a reflecting surface. When light waves encounter a reflecting surface, they are reflected in a direction that is perpendicular to the surface. It explained reflection using the wave nature of light.

Fresnel equations

The Fresnel equations are used to calculate the amount of light that is reflected from a reflecting surface. The equations take into account the angle of incidence, the refractive index of the material, and the thickness of the reflecting surface.

Maxwell Electromagnetic Theory

The Maxwell Electromagnetic Theory is used to explain the behavior of light in all situations. The theory takes into account the electric and magnetic fields that are associated with light waves.

Newton’s Corpuscular Theory Light

It consists of very small invisible elastic particles which travel in vacuum with a speed of 3 x 108 m/s. The theory could explain reflection and refraction. The size of corpuscular of different colors of light are different. It could not explain interference, diffraction, polarization. photoelectric effect and Compton effect. The theory failed as it could not explain why light travels faster in a rarer medium than in a denser medium.