Lenses - Practice Problems
If you can do these,
You will do well!
Read Holt Pages 494-505
Mathematical prediction of image
Location
Where f is the
focal length do is the
object distance, and
di is the image
distance
Height
Where hi is
the image height,
ho is the object
height, and di is
the image
distance, and do
is the object
distance
Magnification
Where hi is
the image height,
ho is the object
height, and di is
the image
distance, and do
is the object
distance
Sign Conventions for Lenses
• Convergent lenses always have positive Focal
Lengths (f-values)
• Divergent lenses always have negative Focal
Lengths (f-values)
• The object distance is always positive (and
defines the ‘front’ of the lens)
• The Image will be positive if it is real and
negative if it is virtual.
The Variables Used
• f – Focal length
• Focus (name of location)
• do – Object distance
• di – Image distance
• C – Radius of curvature
• Center of curvature (location)
• These values are distances.
The principle axis can be
considered a number line
for which the lens is the
origin and the object
determines the negative
side of the number line
• ho – Object height
• hi – Image height
• m – Magnification
• All of these values are
concerning the object or
image. A positive value
indicates the image (or
object) is upright and a
negative is inverted. The
magnification value is
analogous to a percentage:
less than 1 is a shrunken
image, greater than 1 is
enlarged
A converging lens has a Focal length of 15.0cm and a
20cm tall object is placed 23.0 cm from the lens.
A. What is the image distance?
B. Is the image: Real or Virtual, Enlarged or Reduced,
Upright or Inverted?
C. What is the image height?
D. What is the magnification of the image?
E. Draw the scenario to show the lens, object and image
as well as the three principle rays.
A. 43.125cm B.R,E,I
C. -37.5cm D.-1.875
Problem #1
A converging lens has a Focal length of 8.0cm and a
5.0cm tall object is placed 2.0 cm from the lens.
A. What is the image distance?
B. Is the image: Real or Virtual, Enlarged or Reduced,
Upright or Inverted?
C. What is the image height?
D. What is the magnification of the image?
E. Draw the scenario to show the lens, object and image
as well as the three principle rays.
A. -2.67cm B.V,E,U C.6.67cm D. 1.33
Problem #2
A diverging lens has a Focal length of 10.0cm and a
8.0cm tall object is placed 6.0cm from the lens.
A. What is the image distance?
B. Is the image: Real or Virtual, Enlarged or Reduced,
Upright or Inverted?
C. What is the image height?
D. What is the magnification of the image?
E. Draw the scenario to show the lens, object and image
as well as the three principle rays.
A. -3.75cm
B. V,R,U
C. 5cm
Problem #3
D.0.625
A diverging lens has a Focal length of 8.0cm and a
5.0cm tall object is placed 10.0cm from the lens.
A. What is the image distance?
B. Is the image: Real or Virtual, Enlarged or Reduced,
Upright or Inverted?
C. What is the image height?
D. What is the magnification of the image?
E. Draw the scenario to show the lens, object and image
as well as the three principle rays.
A. -4.44cm B. V,R,U C. 2.22cm D. 0.444
Problem #4