<< Chapter < Page Chapter >> Page >
P = 1 f . size 12{P= { {1} over {f} } } {}

Power P size 12{P} {}

The power P size 12{P} {} of a lens is defined to be the inverse of its focal length. In equation form, this is

P = 1 f . size 12{P= { {1} over {f} } } {}

where f size 12{f} {} is the focal length of the lens, which must be given in meters (and not cm or mm). The power of a lens P has the unit diopters (D), provided that the focal length is given in meters. That is, 1 D = 1 / m , or 1 m 1 . (Note that this power (optical power, actually) is not the same as power in watts defined in Work, Energy, and Energy Resources . It is a concept related to the effect of optical devices on light.) Optometrists prescribe common spectacles and contact lenses in units of diopters.

What is the power of a common magnifying glass?

Suppose you take a magnifying glass out on a sunny day and you find that it concentrates sunlight to a small spot 8.00 cm away from the lens. What are the focal length and power of the lens?

Strategy

The situation here is the same as those shown in [link] and [link] . The Sun is so far away that the Sun’s rays are nearly parallel when they reach Earth. The magnifying glass is a convex (or converging) lens, focusing the nearly parallel rays of sunlight. Thus the focal length of the lens is the distance from the lens to the spot, and its power is the inverse of this distance (in m).

Solution

The focal length of the lens is the distance from the center of the lens to the spot, given to be 8.00 cm. Thus,

f = 8.00 cm.

To find the power of the lens, we must first convert the focal length to meters; then, we substitute this value into the equation for power. This gives

P = 1 f = 1 0 . 0800 m = 12 . 5 D. size 12{P= { {1} over {f} } = { {1} over {0 "." "0800"" m"} } ="12" "." 5" D"} {}

Discussion

This is a relatively powerful lens. The power of a lens in diopters should not be confused with the familiar concept of power in watts. It is an unfortunate fact that the word “power” is used for two completely different concepts. If you examine a prescription for eyeglasses, you will note lens powers given in diopters. If you examine the label on a motor, you will note energy consumption rate given as a power in watts.

Got questions? Get instant answers now!

[link] shows a concave lens and the effect it has on rays of light that enter it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens). The concave lens is a diverging lens    , because it causes the light rays to bend away (diverge) from its axis. In this case, the lens has been shaped so that all light rays entering it parallel to its axis appear to originate from the same point, F size 12{F} {} , defined to be the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length f size 12{f} {} of the lens. Note that the focal length and power of a diverging lens are defined to be negative. For example, if the distance to F size 12{F} {} in [link] is 5.00 cm, then the focal length is f = –5.00 cm and the power of the lens is P = –20 D size 12{P"=-""20"" D"} {} . An expanded view of the path of one ray through the lens is shown in the figure to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and be diverged.

The figure on the top shows an expanded view of refraction for ray 1 falling on a concave lens. The angle of incidence is theta 1 and angle of refraction theta 2. The ray after the refraction at the second surface emerges with an angle equal to theta 1 prime with the perpendicular drawn at that point. Perpendiculars are shown as dotted lines. The figure at the bottom shows a concave lens. Three rays, 1, 2, and 3, are considered. Ray 2 falls on the axis and rays 1 and 3 are parallel to the axis. Rays 1 and 3 after refraction appear to come from a point F on the axis. The distance from the center of the lens to F is small f and is measured from the same side as the incident rays. Ray 2 on the axis goes undeviated.
Rays of light entering a diverging lens parallel to its axis are diverged, and all appear to originate at its focal point F size 12{F} {} . The dashed lines are not rays—they indicate the directions from which the rays appear to come. The focal length f size 12{f} {} of a diverging lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 8

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask