Waves and Optics [Tutorials] (FSCT3209)

Computer Science - COS

Semester: Second Semester

Level: 300

Year: 2016

Answers (200 )
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OPTICS TUTORIAL QUESTIONS
Exercise 1
The domain of visible light is approximately defined by: 400nm ≤
0
≤ 750nm, λ
0
being the
wave length of the radiation in the vacuum.
1.1 What is the corresponding domain of frequency in ( H z )
1.2 Give the corresponding domain of energy in (J) and in (eV )
1.3 Is a radiation with energy E = 3.8eV perceptible by human beings?
1.4 What is the corresponding domain of wave length
n
(in nm) in a medium with index of
refraction n = 1.658?
N.A: C = 3.10
8
m/s; h = 6.62.10
-34
J.s ; 1eV = 1.610
-19
J.
Exercise 2
1- Taking the plane of the figure as the plane of incidence, the incident point 1 is at the boundary
surface of two media of index of refraction m and n
2
. Draw two half circles of centre I and of
radius m and n
2
in the medium 2.
2- The extension of the incident ray intersect the half circle of radius nj at point A and the
perpendicular through A at the tangent at I at the boundary intersects the circle of radius n
2
at
point B,
2.1- Recover from this figure the Snell’s relation.
2.2- Deduce that IB is the refracted ray.
2.3- Discuss according to the relative values of n
1
and n
2
.
Exercise 3
Consider two plane mirrors making an angle of 45°. Suppose that an incident ray undergoes one
reflection on each of the mirrors. Determine the deviation, that is, the angle between the
directions of the incident and emergent rays.
Exercise 4
Calculate the limit value i
0
of the angle of incidence for which a light ray is transmitted from a
prism of angle A= 60° and of index of refraction n = 1.52.
Exercise 5
1- Draw a prism of angle A an index of refraction n.
2- Insert the angles i
1
r
1 ;
i
2
, r
2
and the angular deviation D produced by the prism.
3- Write the relations .of the prism.
4- Study the deviation as a function of the index of refraction.
5- At which condition on the angle of incidence a luminous ray could emerge from the prism?
6- Calculate the limit value i
0
of the angle of incidence, Take A= 60°; n = 1.52
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Exercise 6
1. Show that when a plane mirror moves at a distance d, the image of an object moves at a
distance 2d.
2. Show, that when a plane mirror turns of an angle
the image of an object turns of 2.
Exercise 7:
Consider an object AB in front of a concave spherical mirror before its centre C;
1) -Determine by geometrical construction, the position and the nature of the image A’B’ of the
object in the mirror.
2) -Write the equations of the system and the transverse magnification taking the vertex V of the
mirror as origin for algebraic measures.
3) -Deduce the relations of the system taking C as the origin for algebraic measures.
4) -Determine the transverse magnification when C is taken as origin for algebraic measures.
Exercise 8
Consider two spherical mirrors, one concave and another convex.
1- Indicate in each case the position of the centre of curvature
C
and the reflecting surface.
2- Consider an object
AD
in front of the concave spherical mirror, before its centre
C.
2.1- Determine by geometrical construction, the position arid the nature of the image
A ’B’
of the
object in the mirror.
2.2- Write the equations of the system taking the vertex 7 of the mirror as origin for algebraic
measures.
2.3- Determine the transverse magnification when
V
is taken as origin for algebraic measures.
3. The object AB is situated at 15cm in front of the mirror with, focal distance +5cm. The
magnitude of the object is 2cm.
3.1 -Find the position and the magnitude of the image.
3.2- Is the image real? upright? '
What is its transverse magnification?
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