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1.   A sheet of glass of refractive index ng = 1.5 is in contact with water.
    Refractive index of water nw = 1.33.
    A ray of light meets the air/glass interface at an angle of incidence, i = 40°, as shown below.
     
   
  a) Calculate the angle of refraction, r2 in the water.
  b) Calculate the critical angle of incidence for the glass/water interface.
     
2.   Light is incident at one end of a transparent plastic rod, as shown below.
The refractive index of the plastic is 1.4
     
   
     
    Find the maximum value of the angle of incidence, i, which will result in total internal reflection at point A.
     
3. A ray of light is refracted through a prism.
    The angle of the prism, A = 70°.
    The angle of refraction in the glass at the first face is 28°.
     
   
    Calculate
  a) the angle of incidence in the glass at the second face
  b) the angle of incidence at the first face and the angle of refraction at the second face given that the refractive index n=1.4
  c) the angle of deviation of the ray.
     
4.   A ray of light is incident normally, at the mid point of one face of a prism as shown below.
    The refractive index of the prism material is n = 1.5 and the refracting angle is 50°.
     
   
     
  a) Calculate the critical angle for the material of the prism.
  b) Draw a diagram which shows the path of the ray through the prism.
  c) Calculate the angle of refraction when the ray emerges from the prism.
     
5. a) In the context of light passing through prisms, define
    i)  deviation
    ii) dispersion
  b) A prism has an angle of 30° at its apex, as shown below.
    Yellow light of wavelength 575nm is incident normally on the left face of the prism as shown below.
    The prism has a refractive index of 1.50 for this wavelength.
    What is the deviation of this light beam as it passes through the prism?
     
   
     
  c) Assume that a prism, made from the same glass, has three 60° angles.
    Yellow light of wavelength 575nm is incident normally on one side.
    Draw a diagram showing the path of this light through the prism.
     
6.   An object is 10cm below the surface of water (refractive index nw = 1.33).
    An observer is vertically above the object, as shown below.
    Calculate the apparent depth of the object.
     
     
     
7. An object is under a piece of glass of thickness 10cm.
    The glass in under water.
    An observer is in the water vertically above the object as shown below.  
     
     
     
    The refractive index of the glass is ng = 1.5 and the refractive index of water is nw = 1.33.
    Calculate the apparent depth of the object below the surface of the glass.  
     
8.    A small metal ball is falling with it’s terminal speed through water.
    The terminal speed for the ball is known to be 10cms-1
    An observer watches the falling ball from above (outside the liquid).
    At what speed will this observer see the ball falling?     
     
9.    An object is at a depth R below the surface of water.
    Oil of refractive index no is poured onto the surface of the water until the layer of oil has a thickness t, as shown below.
    The observer is vertically above the object. 
     
     
     
    It is not possible to draw a ray for this situation to scale on the diagram above (the angles are very small) but the following diagram shows approximately how light passes from a point on the object to the observer’s eye. 
     
     
     
    Show that the relation between R (the real depth of the object below the surface of the water) and A (the apparent depth of the object below the surface of the oil) is given by: 
   
     
10. a) Describe briefly the simplest way to make an approximate measurement of the focal length of a convex lens.
  b) Explain why the same method can not be used for a concave lens.
  c) A convex lens is used to obtain an image of the moon on a screen.
    The focal length of the lens is 30cm.
    The radius of the moon’s orbit around the earth is about 382400km and the radius of the moon is about 1740km.
Calculate the radius of the image of the moon on the screen.
11.   An object 2cm high is placed 4cm from a convex lens of focal length 6cm.
    For simplicity, assume that the object is placed on the principal axis of the lens.
  a) Draw a ray diagram, to scale, to find the position, type and size of the image formed by the lens.
  b) Check your answers by calculation.
     
12.   An object 3cm high is placed 6cm from a concave lens of focal length 8cm.
    For simplicity, assume that the object is placed on the principal axis of the lens.
  a) Draw a ray diagram, to scale, to find the position, type and size of the image formed by the lens.
  b) Check your answers by calculation.
     
13.   An object 2cm high is placed on the principal axis, 5cm away from a convex lens of focal length 5cm.
    Draw a ray diagram to show how this lens forms an image of the object.
    What type of image is formed and what is the image distance?
     
14.   A converging lens forms an image of an object on a screen, as shown below.
     
    A diverging lens is then placed as shown in the next diagram 
     
     
    A clear image is formed when the screen is placed at 30cm from the concave lens.
    Calculate the focal length of the diverging lens.  
     
15.    A convex lens has a focal length, f1 = 15cm.
    A concave lens has a focal length, f2 = 20cm.
    The two lenses are placed 5cm apart as shown below.
    The two lenses are used to form a real image of a distant object (not shown on the diagram, object distance > 25m).
     
    Calculate the image distance, v.
     
16.   Light of wavelength 450nm is directed towards a diffraction grating.
The first order image(s) are at 25° to the normal to the grating.
Calculate
  a)  the number of lines per mm of the grating
b) the angle of the next image
  c) the maximum number of images (theoretically) visible with this grating and wavelength of light.
17.   Draw intensity/position diagrams for
  a) the diffraction pattern formed by a single slit of width about 100μm
  b) the diffraction pattern formed by two slits of about 100µm width separated by about 200μm.
     
18.   Light of wavelength 600nm is directed towards a single slit of width 80μm.
    A diffraction pattern is observed on a screen placed 1.5m away from the slit.
    Calculate the width of the central maximum of the diffraction pattern.
19.   A wedge shaped film is created by placing a thin piece of wire between two sheets of glass.
    The film is illuminated by light from a sodium lamp (λ = 590nm).
    The diagram below represents the interference pattern observed through a microscope.
     
    The distance x is found to be 2.5mm.
    If the length of the two pieces of glass is 4cm, calculate the diameter of the piece of wire.
     
20.    Two stars are viewed through a telescope having an objective of diameter 50mm.
    It is found that the telescope can just resolve the two images of the stars.
    If the stars are both 15 light years away from the earth, estimate the distance between them.
     
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