


1. 

A sheet of glass of refractive index n_{g} = 1.5 is in
contact with water. 


Refractive index of water n_{w} = 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, r_{2} 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 n_{w} = 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 n_{g} = 1.5 and the
refractive index of water is n_{w} = 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 n_{o} 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, f_{1} = 15cm. 


A concave lens has a focal length, f_{2} = 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. 





return to top of page 