questions regarding lenses and mirror

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Summary: Lenses and Mirrors
Equations (1)
Lenses redirect light by refraction. Converging
lenses are thicker in the middle and bring light rays
together. Diverging lenses are thinner in the middle
and spread light out.
Lens terminology is very similar to that of mirrors.
An important difference is that when we consider a
single lens, virtual images appear on the same side of
the lens as the object, and real images appear on the
opposite side. Another difference is that lenses have
a focal point on each side.
Ray diagrams for converging and diverging lenses
are also similar to those for mirrors.
And like mirrors, lenses have equations that quantify
the relative size, orientation and distance of the
images they produce. In addition, the lensmaker’s
equation determines the focal length of a lens with
differing radii of curvature on its two sides. Sign
conventions can be trickier for lenses, so pay special
attention to them.
Several lenses can be used together to enhance their
magnification properties, such as in a refracting
In a microscope, a lens called the objective creates a
real image, which is used as the object for a second
lens called the eyepiece. The viewer looks into the
eyepiece and sees a final image that is inverted,
virtual, and magnified.
The human eye contains a lens that can change shape
in order to create a focused image on the lightsensitive retina at the back of the eye. A person’s
near point and far point are the closest and farthest
distances on which she can focus.
Sometimes a lens is specified by its refractive power,
which is the inverse of its focal length. Refractive
power P is measured in diopters, where 1 diopter =
1 m-1. This unit is commonly used with eyeglasses
and contact lenses.
The angular size of an object is the angle of the field
of view that is taken up by the object. It is measured
in radians, which allows the use of a small-angle
approximation: For small angles, the angular size of
an object is approximately its height divided by its
The angular magnification of a simple magnifier is
the ratio of the angular size of the image to that of
the object when the object is located at the near point
of the human eye.
Lenses can exhibit spherical aberration just as mirrors can. They also exhibit chromatic aberration due to
the differing refractive indices of different wavelengths of light. Both kinds of aberration can cause an
image to look blurry.
You Do (due 11.21.17)
Equations (2)
1. An object is placed between the focal
point of a converging lens and a
distance twice the focal length from the
lens. Draw a ray diagram to determine
the nature of the image and describe the
2. An object is placed in front of a
diverging lens. Draw a ray diagram to
determine the nature of the image.
3. The focal length of a thin lens is
0.110 m. You want to use it to produce
a real image at 0.600 meters from the
lens. How far from the lens should the
object be placed? ( 0.135 m)
4. The cornea and lens of the eye each
refract light as it passes into the eye.
We consider the cornea and lens
together as one thin lens whose shape,
and effective focal length, can be
changed by the muscles around the eye.
When incoming light is parallel, such as
for an infinitely far away object, the eye
muscles shape the effective lens to have
a focal length of about 2.50 cm to
produce a focused image on the retina.
What focal length lens do the muscles
cause to create a focused image of an
object 35.0 cm away? (0.0233 m)
5. A child requires eyeglasses with
diverging lenses, but is concerned that
they will look too thick. The radius of
curvature of the near surface of the lenses has a magnitude of 55.0 cm and the radius of curvature of
the far surface has a magnitude of 35.0 cm. If the lenses are circular with a diameter of 5.00 cm and
a thickness at the center of 0.100 cm, how thick are the glasses at the edge? (0.246 cm)
6. A concave spherical mirror is pointed at the Sun. Its radius of curvature is 2.50 m. The Sun subtends
an angle of 0.533° in the sky. (a) What is the diameter of the image of the Sun created by the mirror?
Hint: Use the magnification equations and the small angle approximation. (b) You want to use the
mirror as a “solar cooker.” If the intensity of sunlight incident on the mirror is 1.00×103 W/m2 and
you want to supply energy to a large cooking pot at a rate of 255 W, what must be the circular
“cross-sectional” area of the cooker? Note that this is not the area of the curved mirror, but of the
planar circle that intercepts the sunlight, the imaginary lid that caps the mirrored bowl. (c) What
intensity is produced at the image?( (a) 1.16 cm (b) 0.255 m2 (c) 2.41e6 W/m2
7. Elizabeth is nearsighted. Without glasses, she can see objects clearly when they are between 15.0 cm
and 90.0 cm away from her eyes. Her glasses are designed to be worn 2.00 cm from her eyes, and
have a focal length so that objects at infinity produce images at her far point. When she is wearing
these glasses, how close to her eye can an object be before it appears out of focus? (17.3 cm)
8. A microscope has an objective lens focal length of 0.30 cm, an eyepiece focal length of 1.3 cm, and
the two lenses are separated by 14 cm. Using an average nearpoint of 25 cm, what is the approximate
overall magnification of the microscope? (-9.0e2)

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