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Numerical Problems From Optics

1. When an object of height 4cm is placed at 40cm from a mirror the mirror forms the image on the object itself. If the height of the image is equal to the height of the object. Find out the focal length of the mirror and identify the mirror.
2. A convergent beam of light passes through a diverging lens of focal length 0.2m and comes to focus at distance 0.3m behind the lens.Find the position of the point at which the beam would converge in the absence of lens?

A problem from Optics

A convergent beam of light passes through a diverging lens of focal length 0.2m and comes to focus at distance 0.3m behind the lens.Find the position of the point at which the beam would converge in the absence of lens?

CBSE 12th Std Physics Numerical from Optics

A convex lens of crown glass(1.5) has a focal length of 15 cm. The lens is placed in (a) water(1.33) and carbon bisulphide(1,65).determine in each case whether the lens behaves as a conveging or a diverging lens and determine its focal length.

Formula used$\LARGE \frac{1}{f}=\left ( \mu _{2} -\mu _{1}\right )\left [ \frac{1}{R_{1}}-\frac{1}{R_{2}} \right ]$$\LARGE \frac{1}{f}=\left ( \mu _{2} -\mu _{1}\right )\left [ \frac{1}{R_{1}}-\frac{1}{R_{2}} \right ]$

For the lens to be converging, f must be positive and for it to be diverging, f must be negative

(a) In water the lens will be converging as the refractive index of glass is greater than that of  water.

(b) In Carbon disulphide the lens is diverging as the refractive index of glass is less than that of CS2

Why Rainbow is in the form of an arc?

Why is a rainbow always bent in the shape of a semi circle…?? but according to the theory light travels straight….!!! (Ramesh asked)

A short introduction to Optics and the Nature of Light

INTRODUCTION

LIGHT is a form of energy which causes the sensation of vision. Optics is the branch of Physics which studies the nature of light and the various phenomena associated with it.

Nature of Light

The nature of light was not at all thought until Newton attempted on it.

Newton’s Corpuscular Theory

According to Sir Isaac Newton light consists of extremely small spherical perfectly elastic particles called corpuscles which are emanating from a source with tremendous speed and whose impact on the retina causes the sensation of vision. This theory could satisfactorily explain the rectilinear propagation and reflection but the explanation given to refraction of light was found wrong later. Newton said that the particles of a denser medium attracted the corpuscles towards them and causes the light to bend at the interface between the two media. If this were correct, light could travel with a greater speed in a denser medium as it would be accelerated more due to the force of attraction by the particles of the denser medium.  But when the velocity of light in different media was found experimentally, it was observed that the velocity of light is less in a denser medium. Further, Newton’s theory could not explain color vision, interference (color in soap bubble and thin films), diffraction (bending of light at sharp opaque obstacles) etc .

Huygens’ Wave Theory

The wave theory proposed by Christian Huygens in 1678 could explain all the above phenomena satisfactorily but failed to explain photoelectric effect (the emission of electrons from the surface of alkali metals when light is incident on it).  Further, Huygens considered light as a longitudinal waves, but the phenomenon of polarization suggests that light is transverse in nature.

Electromagnetic Wave Theory

James Clark Maxwell established the Electromagnetic wave theory in 1864 and he calculated the velocity of electromagnetic waves in vacuum to be 3 x 108 m/s which coincided with the value of experimental value of velocity of light in air. This coincidence led the scientists to conclude that light is an electromagnetic wave.

Dual Nature of Light and Quantum Theory

Even the electromagnetic wave theory could not explain photoelectric effect (for which the particle nature of light is to be used where a ‘light particle’ strikes off an electron from a metal surface). So we have to consider that light has a dual nature; ie, it is a particle as well as a wave at the same time.

According to Max Plank’s Quantum Theory, light is an electromagnetic form of energy emitted as packets called quanta (quantum is the singular form) or photons. The photons possess dual nature.

Introduction to Light – NASA

Light is a form of radiant energy or energy that travels in waves. Since Greek times, scientists have  debated the nature of light. Physicists now recognize that light sometimes behaves like waves and, at other times, like particles. When moving from place to place, light acts like a system of waves. In empty space, light has a fixed speed and the wavelength can be measured. In the past 300 years,
scientists have improved the way they measure the speed of light, and they have determined that it travels at nearly 299,792 kilometers, or 186,281 miles, per second.
When we talk about light, we usually mean any radiation that we can see. These wavelengths range from about 16/1,000,000 of an inch to 32/1,000,000 of an inch. There are other kinds of radiation such as ultraviolet light and infrared light, but their wavelengths are shorter or longer than the visible light wavelengths. When light hits some form of matter, it behaves in different ways. When it strikes an opaque object, it makes a shadow, but light does bend around obstacles. The bending of light
around edges or around small slits is called diffraction and makes patterns of bands or fringes.
All light can be traced to certain energy sources, like the Sun, an electric bulb, or a match, but most
of what hits the eye is reflected light. When light strikes some materials, it is bounced off or reflected. If the material is not opaque, the light goes through it at a slower speed, and it is bent or refracted. Some light is absorbed into the material and changed into other forms of energy, usually heat energy. The light waves make the electrons in the materials vibrate and this kinetic energy or movement energy makes heat. Friction of the moving electrons makes heat.

Question from Wave Optics

What is the difference between interference and diffraction?

Ans:

Interference is caused by the superposition of wave fronts from two coherent sources; But diffraction is caused by the superposition of wavelets from a single wavefront when it confronts an obstacle or a slit.