Ray Optics and Optical Instruments

Reflection of Light by Spherical Mirrors

  • Light is a form of energy which causes sensation of vision.
  • Light is an electromagnetic wave
  • Light travels with a speed of 3 × 108 m/s in vacuum.
  • Light travels with different speeds in different media.
  • In reflection, incident ray, reflected Light ray and normal drawn to the surface lie in the same plane.
  • Angle of incidence = Angle of reflection
  • Angle of deviation = 180 – 2i
  • When the rays reflection if actually converge to the image it is called real image
  • When the light rays appear to diverge from the image it is called Virtual image.
  • Real image can be received on a screen but not the virtual image.
  • From principles of sign conversion all distances are measured. From the pole of the mirror.
  • The distances measured along the direction of incident light one taken as positive and those measured in the direction opposite to the direction of incident light are taken as negative.
  • For spherical mirrors the heights measured upwards and normal to the principal axis are taken as positive & measured downwards are taken as negative.
  • Magnification \tt m = \frac{size \ of \ image}{size \ of \ object}
  • The image formed by a plane mirror is unmagnified, virtual and erect
  • The image is laterally inverted.
  • The minimum height of the plane mirror to observe full height of a person is half the height of that person.
  • If the object moves with a velocity “V” towards or away from the mirror, then image appears to move with a velocity “2V” toward or away from the mirror.
  • When a plane mirror is rotated through an angle “θ” the reflected ray rotates through an angle “2 θ”.
  • Two mirrors are placed at an angle of “θ” the angle of deviation produced by a system = 360° − 2 θ.
  • If the reflecting surface of the mirror is towards the centre of the spherical surface then it is called concave mirror
  • If the reflecting surface of the mirror is away from its centre, then it is called convex mirror.
  • Principal axes is the line joining the pole and the centre of curvature
  • Focal length (f) is the distance between pole and principal focus.
  • Focal length \tt F = \frac{Radius \ of \ curvature}{2}
  • Mirror equation \tt \frac{1}{f} = \frac{1}{v} + \frac{1}{u}
  • If position of object is at infinity – Nature and position of image is Real, Inverted diminished at focus
  • If position of object is beyond centre of curvature Nature and position of image is Real, inverted, diminished between C and F (C = centre of curvature, F = Focus).
  • If position of object is at ‘C’ nature and position of image formed is Real, inverted same size as object at C.
  • If position of object is between focus and pole nature and position of image formed is virtual, Erect, magnified and behind the mirror between pole and focus.
  • If position of object is at focus (F). Nature of Reflected rays are parallel and image formed at infinity.
  • \tt \frac{1}{v} and \frac{1}{u} graph is

  • u-v graph

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1. Images by two inclined plane mirrors : When two plane mirrors are inclined to each other at an angle θ, then number of images (n) formed of an object which is kept between them.
(i)n = \left[\frac{360^{o}}{\theta} - 1\right]; \ {\tt If} \ \frac{360^{0}}{\theta} = even integer
(ii) If \frac{360^{0}}{\theta} = odd integer then there are two possibilities

2. Mirror formula by Spherical mirror Reflection : \frac{1}{f} = \frac{1}{v} + \frac{1}{u}

3. When object lies along the principal axis then its axial magnification m = \frac{I}{O} = \frac{-(v_{2} - v_{1})}{(u_{2} - u_{1})}

4. If object is small; m = -\frac{dv}{du} = \left[\frac{v}{u}\right]^{2} = \left[\frac{f}{f - u}\right]^{2} = \left[\frac{f - v}{f}\right]^{2}