OPTICS

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?

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.

Why the ray of light passing through optical center of a lens passes undeviated while when it passes through other points on the interface of the lens, it gets refracted?

Deviation is the change in direction of the ray while passing through the lens. The middle portion of the lens is comparatively flat and there is a point on the principal axis and inside the sphere through which all the undeviated rays pass.

“Undeviated” doesn’t mean that there is no refraction. When we say that there is no deviation, we only mean that the incident ray and the emergent ray are parallel to each other. For thin lenses, the refraction inside the lens is negligible and therefore we represent the ray passing through the optic centre as a straight line. But in the case of a thick lens, we cannot do so.

(See the diagram)