Department of Physics
University of Lagos
Course: Geometric Optics
B.Sc. (Hons) Degree Program
Code: PHS 227
DUE DATE: 20th April 2023
ATTEMPT ALL
Student Assignment as Part of the Continues Assessment towards the final Grade
1. Explain the following terms:
i.
Specular reflection
ii.
Diffuse reflection
iii.
Index of refraction
iv.
Wave front
v.
Critical Angle
vi.
Total internal reflection
2. The wavelength of the red light from a helium-neon laser is 633nm in air but 474nm in the
aqueous humor inside your eye-ball. Calculate the index of refraction of the aqueous humor
and the speed and frequency of the light in this substance then so that frequency in air is the
same as the frequency in the aqueous humor.
3. A ray of light traveling with speed c leaves point 1 as in the diagram below and is reflected to
point 2. The ray strikes the reflecting surface a horizontal distance x from point 1.
1 Fg x
Fg y1
2
θ1 θ2
Fg y2
Fg l
i.
Show that the time t required for the light to travel from 1 to 2 is
y12  x 2  y 22 | l  x 
2
t
c
ii.
Take the derivative of t with respect to x. Set the derivative equal to zero to
show that this time reaches its minimum value when θ1 = θ2 , which is the law of
reflection and corresponds to the actual path taken by the light this is an example
of Fermat’s Principle of least time.
4. The incident angle θa shown in diagram below is chosen so that the light passes
symmetrically through the prism, which has reflective index n and apex angle A.
A
Fg δ
θa
Fg
θa
θb
θb
i.
Show that the angle of deviation δ ( the angle between the initial and final
directions of the ray) is given by
A
A
 n sin
2
2
(When the light passes through symmetrically, as shown, the angle of deviation is a minimum)
ii.
Use the result of part (i) to find the angle of deviation for a ray of light passing
symmetrically through a prism having three equal angles ( A = 60 o ) and n =
1.52.
iii.
A certain glass has a refractive index of 1.61 foe red light (700nm) and 1.66 for
violet light (400nm). If both colors pass through symmetrically, as described in
part ( i) and if A = 60o , find the difference between the angles of deviation for
the colors.
5. With the aid of a ray diagram for a thin lens, prove that Lensmaker’s equation for a thin lens
 1
1
1 

 n  1 
is:
f
 R1 R2 
Using above, suppose the absolute values of the radii of curvature of a thin lens surfaces are
both equal to 10cm and the index of refraction is n = 1.52. What is the focal length f of the
lens?
sin
6. An object 8.0cm high is placed 12.0 cm to the left of a converging lens of focal length 8.0
cm. A second converging lens of focal length 6.0 cm is placed 36.0 cm to the right of the first
lens. Both lenses have the optic axis. Find the position, size, and orientation of the image
produced by the two lenses in combination.
YOUR PAPER WILL NOT BE GRADED IF SUBMITTED AFTER THE DUE DATE
EXPIRED.