Lecture 16: Geometrical Optics. Reflection Refraction Critical angle Total internal reflection. Polarisation of light waves

Transcription

1 Lecture 6: Geometrical Optics Reflection Refraction Critical angle Total internal reflection Polarisation of light waves

2 Geometrical Optics Optics Branch of Physics, concerning the interaction of light with matter Geometrical Optics- subset of optics concerning interaction of light with macroscopic material Dimension larger than a human hair 50mm Geometrical Optics Light Ray beam of light ray optics Light can travel through empty space, air, glass, water, cornea, eye lens etc. each one referred to as a medium Light rays will travel in a straight line if they remain in the same medium

3 Reflection At the boundary between two media, the light ray can change direction by reflection or refraction Reflection For a mirror (smooth metal surface) all light will be reflected Incident Ray Normal Reflected Ray q i q r Smooth Metal surface

4 Reflection Incident Ray Normal q i q r Reflected Ray Laws of reflection Metal surface. angle of incidence(q i ) = angle of reflection(q r ) 2. Angles measured with reference to the normal to the surface 3. Incident and reflected rays and normal all lie in the same plane Smooth surface: reflection at a definite angle --Specular reflection Incidence Rays Reflected Rays Metal surface

5 Reflection Diffuse reflection Rough Surface No unique angle of reflection for all rays Light reflected in all directions Majority of objects (clothing, plants, people) are visible because they reflect light in a diffuse manner. Normal Incident Ray Reflected Ray q i q r

6 Refraction At the surface of transparent media, glass, water etc both reflection and refraction occur. Refraction (deflection from a straight path in passing obliquely from one medium ( such as air) into another (such as glass) Incident Ray Medium Medium 2 Normal q q q 2 q 2 Reflected Ray Refracted Ray Light ray changes direction going from one medium to another. Which way does it bend and by how much? Is q 2 <q or is q 2 >q Answer Depends on the speed of light in both media

7 Refraction Speed of light in a vacuum: c = 3x0 8 ms - The amount by which a medium reduces the speed of light is characterised by Index of refraction (n) of the medium c n v speed of light in the material = v Indices of Refraction Vacuum (by definition) Air.0003 Glass.52 Water.33 Diamond 2.42 Example Calculate the speed of light in diamond v =c/n =(3x0 8 ms - )/2.42 =.24 x0 8 ms -

8 Refraction Example How long does it take light to travel 394cm in glass Calculate the speed of light in glass c v n 8 30 ms v ms 8 t d v t 3.94m ms 8 s

9 Refraction Monochromatic light (one colour or frequency) Incident Ray Normal Incident Ray Normal Medium q n 2 > n n 2 < n q Medium 2 q 2 q 2 Sinq Sinq v c n v v 2 2 where v and v 2 are the speeds of light in media and 2 respectively Sinq Sin c / n Sinq q n q 2 2 c / n2 Sin 2 n n Sinq n Sinq 2 2

10 Refraction n Sinq n Sinq 2 2 Law of refraction or Snell s law Incident and refracted rays and the normal are all in the same plane product nsinq remains constant as light crosses a boundary from one medium to another

11 Example A laser beam is directed upwards from below the surface of a lake at an angle of 35º to the vertical. Determine the angle at which the light emerges into the air. n (air) =.0003 and n 2 (water) =.33 Snell s law Normal air n q n Sin q n Sin q Sin q.33sin35 0 water n 2 35º.33Sin35 Sinq.0003 Sinq 0.76 q If light enters the water at an angle of , what is its refraction angle in the water?

12 Refraction Monochromatic light (one colour or frequency) Incident Ray Normal Incident Ray Medium q n 2 < n n 2 > n or n 2 > n Medium 2 q 2 Sinq n 2 Sinq n n Sin q n Sin q Normal incidence q = 0 therefore q 2 = 0. transmitted ray is not deviated independent of the materials on either side of the interface.

13 Refraction Real and apparent depth Ruler partially immersed in water air Apparent position of ruler end water ruler End of ruler

14 Refraction Setting sun appears flattened (top to bottom) because light from lower part of the sun undergoes greater refraction upon passing through denser air (higher refractive index) in lower part of the Earth s atmosphere.

15 Critical Angle Refraction n 2 < n q q c >q c q 2 q q c is critical angle as q is increased q 2 increases Angle of incident for which refracted ray emerges tangent to the surface is called the critical angle in this case q 2 = 90 o or Sin q 2 = Sinq Sin n c 2 q 2 n Sinq c n n 2

16 Refraction Total internal reflection n 2 < n q q c >q c Ray undergoes total internal reflection q 2 q when q > q c q c is critical angle incident ray undergoes total internal reflection at boundary and cannot pass into the material with the lower refractive index maximum value of the sine of any angle is Sinq c n n 2 Sinq c total internal reflection occurs at interface only when n 2 < n

17 Example Determine the critical angle for both water and diamond with respect to air. Sinq c Refraction n n 2 water q c n.0003 sin sin 49 n diamond q c n.0003 sin sin 24.4 n

18 Example What happens to light ray at the glass-air interface in prism as shown. Refractive index of glass =.52 Refractive index of air = º Glass prism (right angled isosceles triangle) n.33 qc sin sin 6 n n.0003 qc sin sin 4 n Total internal reflection at glass air interface if incident angle is >4 0 What happens the beam if the prism is immersed in water? Refractive index of water =.33 q c > 45º Critical angle given by 45º Total internal reflection at glass-water interface does not occur

19 Refraction Total internal reflection Applications diameter of core 8mm Optical fibre (end on) Refractive index of core greater than refractive index of clading Light coupled into core will travel extremely long distances along fibre, undergoing total internal reflection at core-cladding interface and exit only at the other end. Fibre optic cables used for telecommunications and for diagnostic tools in medicine

20 Example Light in air is incident on a glass block at an angle of 35 0 The sides of the glass block are parallel. At what angle does the light emerge into the air from the lower surface of the glass block? 35 0 q 2 air glass block has parallel sides, glass therefore q 3 = q 3 q 4 Using Snell s Law n Sinq air Sinq q q 2 Let n = refractive index of air & n 2 = refractive index of glass 35 0 n Sinq 2 2 n Sin n Sinq n Sinq n Sinq Since q 3 = q n Sin35 n Sinq 4 Sin35 0

21 Light: Electromagnetic wave Visible spectrum Infrared Wavelength Ultra violet Electromagnetic wave Transverse wave v f V: velocity f: frequency : wavelength Electromagnetic wave

22 Polarised Light Schematic representation Light beam Polariser Light source Light waves vertically polarised Unpolarised light viewed along direction of propagation polarised light viewed along direction of propagation Unpolarised light Polaroid filter Polarised light

23 Polarised Light Schematic representation Vertical polariser Unpolarised Incident beam Horizontal polariser Vertically polarised light wave Unpolarised light Polarising filter Polarised light

24 Polarised Light Light can become polarised by Reflection refraction scattering Unpolarised incident light Polarised reflected light?? Polarised incident light Polarised reflected light Polarised incident light No reflected light

25 Polarised Light Applications 3D movies 2 cameras, a short distance apart, photograph original scene 2 slightly different images projected on screen Each image linearly polarised in mutually perpendicular direction 3D glasses have perpendicular polarisation axis Each eye sees a different image associated with different viewing angle from each camera Brain perceives the compound image as having depth or three dimensions.

26 Polarisation of light : application Application to dentistry Early detection of caries Visual, mechanical probing, x rays??? Demineralised enamel viewed directly with unpolarised light No information Demineralised enamel is polarisation sensitive Polarised light incident on the dental tissue shading may be seen, indicating the early stages of caries at the tooth s surface

27 Example The wavelength of red light from a HeNe laser is 633 nm but is 474 nm in the aqueous humor inside an eyeball. Calculate the index of refraction of the aqueous humor and the speed and frequency of the light in the substance. c f 0 n c v f Refractive index n 0 633n 633nm 474nm 0 Speed in aqueous humor 8 c 3x0 ms v 2.25x0 ms n.34 v 2.25x0 ms 474x0 m 0 f 8 Frequency of the light in aqueous humor 8 4 f 4.75x0 Hz 9 Frequency of the light in air c 3.00x0 ms 8 4 f0 4.75x0 Hz x0 m.34