Ray Optics

Mirrors
Laws of Reflection

Spherical Mirror
A spherical mirror is a curved reflecting surface. It is painted with silver coating on one side, so that it reflects light that is incident on it. The reflected ray always passes through the focus, because the mirror is curved.

F = R/2 ; where F is the focus & R is the radius of Curvature.

Concave Mirror

Convex Mirror

Mirror Formula
1/f = 1/u + 1/v

Sign Conventions :

Follow the cartesian system ; Pole at the Origin ; Distances to the left and bottom will be negative and distances to the right and top will be positive.

Lenses
Lenses are curved Refracting Surfaces. The refraction takes place such that the refracted ray always passes through the primary focus, since the lens is curved.

Concave Lens

Convex Lens

Plano Convex & Concave Lenses : These lenses have only one hemispherical Surface.

Lens Formula
1/f = 1/v - 1/u

Sign Conventions :

Follow the cartesian system ; optical center at the Origin ; Distances to the left and bottom will be negative and distances to the right and top will be positive.

Lens Maker's Equation
1/f = (μ2 - 1)[ 1/R1-  1/R2]

Where R1 and R2are radius of curvatures of the two surfaces.

For Plano Convex lens, one surface is straight , thus Radius of curvature for on surface is infinity.

Magnification
Magnification = h2/h1 = v/u

Power of Lens
Power of Lens = 1 / f

Power of lens is measured in Dioptres, if the focal length is in metres.

Vision Correction
Myopia

Myopia is near Sightedness. A concave lens of suitable focal length is used for vision correction.

Hypermetropia

Hypermetropia is far sightedness. A convex lens of suitable focal length is used for vision correction.

Presbyopia

Presbyopia is the condition of weak eye sight for distant as well as for nearby objects. A bifocal lens is used for vision correction.

Optical Instruments
Optical instruments are used to either magnify objects nearby or to view distant objects. The arrangement of lenses matters in these instruments. The Distance of Distinct Vision (DDV) is the minimum distance upto which an object can b seen clearly. The DDV is said to be 25 cm.

Magnifying Power = Angle subtended at eye by image / angle subtended at eye by object at DDV

Simple Microscope
Magnifying Power = β/α

Magnifying Power = D/v + D/f

Thus, magnifying power of Simple Microscope could be anything from D/f to 1 + D/f

Compound Microscope


Magnifying Power = β/α

Magnifying Power = - {vo/ uo}{1 + D/fe}

Telescope
Magnifying Power = - fo/fe

Tips And Tricks

 * 1) The number of images formed by two mirrors inclined at an angle x is [360/x] - 1.