Exercise 1

Determine the image produced by a converging lens of an object placed 4 cm away from the lens.
and having a size of 2 cm. The focal distance is 3 cm. Drawing: take 1 square for
1 cm.

Exercise 2
An object 2 cm long is located 3 cm from a converging lens whose focal length
is 4 cm. Determine the image given by the lens. Drawing: take 1 square for 1 cm.

Exercise 3
An object with a size of 15 cm is placed at a distance of 60 cm from a lens.
converging lens with a focal length of 40 cm. Determine the image. Drawing: take 1 square for
10 cm.

Exercise 4
A converging lens has a focal length of 6 cm. An object with a size of 4 cm.
is placed at the distance of the lens. Determine the image.
d = 3 cm

Exercise 5
A camera lens is focused on a group of people. The closest is 3 meters away.
the furthest at 8 m. The focal length of this lens is 5 cm, where should the film be located?
for clear images to form on it?

Exercise 6
To photograph objects 5 meters away, the lens of a certain device must be at 11
cm of the film. Where should it be to have clear images of objects 4 m away?

Exercise 7
A slide projector for 24 mm x 36 mm slides has a lens with a focal length of 7.5 cm.
The device is 5 m from the screen. What are the dimensions of the image?

Exercise 8
We have a square screen with sides of 2 m. We want to project slides of 24 mm x
36 mm and place the projector 12 m from the screen. What should be the focal length of
the goal is for the image to be as large as possible, but not to overflow from the screen?
Exercise 9
The objective of a camera has a focal length of 5 cm. The format of the film is
of 24 mm x 36 mm. We want to photograph a painting whose dimensions are 2 m x 3 m. To
How far from the board should the device be placed for the image of the board to fill the entire
available seat for the movie?

Exercise 10
Determine the image of an object 4 cm long, placed 4 cm from a diverging lens whose
The focal length is 12 cm. Drawing: take 1 square for 1 cm.

Exercise 11
A diverging lens has a focal length of 6 cm. An object with a size of 4 cm
d = 2 cm. Determine the image.
cm. d)d= 12 cm.

Exercise 12
A divergent lens has a focal length of 15 cm. We observe an image at 6 cm from the lens.
Lens. This image has a size of 18 mm. Where is the object and what is its size?

Exercise 13
At what distance from a lens should an object be placed to obtain a virtual image five
times larger and located 30 cm from the lens? What are the characteristics of the
lentil?

Exercise 14
A candle is located 3 m from a wall. We want to place a lens 75 cm from the candle.
In order to have a real image on the wall. Which lens should be taken?

Exercise 15
An object is located 4 m from a screen. Using a lens, we would like to obtain on it
an image three times larger than the object. What should be the focal length of the lens and
Where should this one be placed? Do the calculation and the construction.
Exercise 16
We have a converging lens with a focal length of 20 cm. Where should an object be placed if we want it to...
Is the image real and the same size as the object?

Exercise 17
A candle is located 2 m from a wall. We have a converging lens whose
The focal length is 32 cm. Where should it be placed to obtain a real image on the wall?
the candle? The flame is 3 cm high. What is the height of its image? Study all the
solutions.

Exercise 18
At what distance from a converging lens with a focal length of 16 cm should one place a ...
Light object to obtain a real image four times larger?

Exercise 19
A diverging lens has a focal length of 20 cm. Where should a real object be placed to achieve...
obtain a virtual image half the size of the object?

Exercise 20
An object is located 10 m from a screen. What lens should be used to form an image on the screen?
a real image 20 times larger than the object and where should it be placed?

Exercise 21
At what distance from a converging lens with a focal length of 18 cm should an object be placed to
obtain an image flipped three times larger? What is the nature of the image?

Exercise 22
An eye is located 2 cm from a pair of glasses. Someone observing this eye through the glasses
The lens sees an image that is 10% smaller than the eye. Determine the characteristics of the lens.
of glasses.

Exercise 23
We want to build a glass lens (N= 1.5), with a focal length of 40 cm.
Two faces must be convex and have the same radius of curvature. What is the value of this?
last?
Exercise 24
A lens has a refractive index of 1.55. One of its surfaces is convex and has a radius of
curvature of l m. The other side is concave and has a radius of curvature of 1.5 m. What is the
focal length?

Exercise 25
The radii of curvature of a lens are 20 and 25 cm. Calculate the convergence and the
focal length of this lens if it is biconvex, if it is biconcave, if it is a
meniscus with a thin edge and if it is a meniscus with a thick edge. The refractive index is 1.6.

Exercise 26
A divergent beam is transformed by a lens into a convergent beam. The two
Bundles are cones of revolution with a base radius of 4 cm. The angle between the
the generator and the axis is 100 for the divergent beam and 200 for the convergent beam.
Determine the characteristics of the lens.

Exercise 27
In a converging conical beam, the largest angle between the rays is 24°. This
A beam arrives on a diverging lens with a focal length of 20 cm. The intersection
the beam with the lens is a disk 4 cm in diameter. Study the beam that comes out of
the lens. Calculate the angle formed by the widely spaced rays.

Exercise 28
A parallel beam of light, shaped like a cylinder with a diameter of 5 cm, falls on
a lens. It emerges as a divergent beam in which the rays that border the beam
makes an angle of 4° with the axis. The lens is made with glass whose refractive index
worth 1.5. It has a convex side and a concave side. Find a pair of values
possible for the lens curvature radii.

Exercise 29
We attach two converging lenses and one diverging lens whose focal lengths are
respectively 4, 12, and 6 cm. What is the focal parameter of the system?

Exercise 30
Which lens should be attached to a converging lens of 5 diopters to obtain a
system with a focal length of 50 cm?
Exercise 31
A simplified microscope consists of two converging lenses, the objective and the eyepiece.
with focal lengths of 0.99 mm and 5 cm respectively. These lenses are coaxial.
and located 14 cm apart from each other. An object with a size of 0.1 mm is located 1 mm away.
from the objective. Calculate the position and size of the image seen in the eyepiece.