Light and Optics

 

This chapter is about refraction of light, total internal reflection, image formation by lenses, thin lens formula, optical instruments and image formation by spherical mirrors.

 
6.1 Refraction of light
 
  Refraction of light  
 

The bending of a light ray at the boundary of two medium as the light ray propagates from a medium to another with difference optical density.

 
     
 

The speed and direction of light changes when in different medium

 
     
 
  • Light that moves from less dense to denser medium will refracted towards normal.
  • Otherwise, the light that moves from denser to less dense medium will refracted away from normal.
 
  Formula for refraction index, n  
 
  • \(n=\dfrac{\text{sin i}^0}{\text{sin r}^0}\)

 (Snell's law), where \(\text{i}^0\) = incidence angle, \(\text{r}^0\) = refracted angle

 
 
  • \(n=\dfrac{D}{d}\), where D = real depth, d = apparent depth
 
 
  • \(n=\dfrac{c}{v}\)

 where c = velocity of light in air (\(3\times10^8\text{ms}^{-1}\)), v = velocity of light in a medium

 
 
  • \(n=\dfrac{1}{\text{sin c}^0}\)

 where \(\text{c}^0\) = critical angle

 
     
 
 
6.2 Total Internal Reflection
 
  Total Internal Reflection  
 

Reflection of light rays at the border of two medium when the angle of incidence in an optically denser medium is greater than the critical angle.

 
     
 
  The critical angle, c  
 

 The maximum angle of incidence before the total internal reflection can occur

(\(r^0=90^0\))

 
     
 

Conditions for total internal reflection:

  • i > c
  • light moves from denser \(\rightarrow\) less dense medium
 

Examples of total internal reflection:

  • Mirage
  • Prism periscope
  • Prism binocular
  • Fiber optics
 
 
6.3 Image Formation by Lenses
 
 

Characteristics of image

  • Enlarged
  • Diminished
  • Same size
  • Inverted
  • Upright
  • Virtual
  • Real
 

Lenses

  1. There are 2 types of lenses, namely the

    • Convex lens

    • Concave lens

  2. Light rays passing through a convex or converging lens are bent towards the principal axis, whereas rays passing through a concave or diverging lens are bent away from the principal axis.

 
  Linear magnification, m  
  Ratio of image height to object height (no unit)  
     
  \(m=\dfrac{h_i}{h_o}\), where \(h_i = \) image height,  \(h_o = \) object height  
     
  \(m=\dfrac{v}{u}\), where \(v =\) image distance, \(u=\) object distance  
     
 
 
6.4 Thin Lens Formula
 
  Lens equation relating \(f\,,u\,,v\)  
 

 \(\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\), where f = focal length, u = object distance, v = image distance

 
     
 
  \(+\) \(-\)
\(f\) convex lens (converging) concave lens (diverging)
\(v\) real image virtual image (same side with object)
 
 
6.5 Optical Instruments
 
Microscope Telescope

Similarities

  • Two convex lenses
  • First image (the object of the eyepiece: reals, inverted
  • Final image: virtual, inverted, magnified

Differences

Lens type: 2 high-powered lens

Lens type: 1 high(eyepiece), 1 low-powered lens

Focal length: \(f_0 < f_e\)

Focal length: \(f_0 > f_e\)

First image: enlarged

First image: diminished

Position of final image: close to the eye

Position of final image: infinity

Distance between the lens: \(D>f_0+f_e\)

Distance between the lens: \(D=f_0+f_e\)

Magnification: \(M=m_0\times m_e\) Magnification: \(M=\dfrac{f_0}{f_e}\)
 

Applications of Small Lenses in Optical Instrument Technology

 
  • small lenses are used in smartphone cameras and CCTV
  • uses small size convex lens
  • produce real, inverted and diminished image at the sensor
  • to produce image with such characteristics (R, I, D) the distance between sensor and centre of lens has to be at least the length of focal length of lens
 
 
6.6 Image Formation by Spherical Mirrors
 

Field of vision

  • Plane mirror - narrow
  • Concave mirror - very narrow
  • Convex mirror - wide
 
Concave mirror Convex mirror
  • C - Centre of curvature 
  • r - Radius of curvature
  • F - Focal point
  • f - Focal length
  • u - Object distance
  • v - Image distance
 

Applications of Concave Mirrors in Daily Life:

  • Cosmetic mirror
  • Dental mirror
  • Reflector in car headlight
 

Applications of Convex Mirrors in Daily Life:

  • Blind spot mirror
  • Security mirror in buildings
  • Vehicle rear mirror