<< Chapter < Page Chapter >> Page >
m = m o m e , size 12{m=m rSub { size 8{o} } m rSub { size 8{e} } } {}

where m o is the magnification of the objective and m e is the magnification of the eyepiece. This equation can be generalized for any combination of thin lenses and mirrors that obey the thin lens equations.

Overall magnification

The overall magnification of a multiple-element system is the product of the individual magnifications of its elements.

Microscope magnification

Calculate the magnification of an object placed 6.20 mm from a compound microscope that has a 6.00 mm focal length objective and a 50.0 mm focal length eyepiece. The objective and eyepiece are separated by 23.0 cm.

Strategy and Concept

This situation is similar to that shown in [link] . To find the overall magnification, we must find the magnification of the objective, then the magnification of the eyepiece. This involves using the thin lens equation.

Solution

The magnification of the objective lens is given as

m o = d i d o ,

where d o size 12{d rSub { size 8{o} } } {} and d i size 12{d rSub { size 8{i} } } {} are the object and image distances, respectively, for the objective lens as labeled in [link] . The object distance is given to be d o = 6.20 mm , but the image distance d i is not known. Isolating d i , we have

1 d i = 1 f o 1 d o , size 12{ { {1} over {d rSub { size 8{i} } } } = { {1} over {f rSub { size 8{o} } } } - { {1} over {d rSub { size 8{o} } } } } {}

where f o size 12{f rSub { size 8{o} } } {} is the focal length of the objective lens. Substituting known values gives

1 d i = 1 6 . 00 mm 1 6 . 20 mm = 0 . 00538 mm . size 12{ { {1} over {d rSub { size 8{i} } } } = { {1} over {6 "." "00 mm"} } - { {1} over {6 "." "20 mm"} } = { {0 "." "00538"} over {"mm"} } } {}

We invert this to find d i size 12{d rSub { size 8{i} } } {} :

d i = 186 mm. size 12{d rSub { size 8{i} } ="186 mm"} {}

Substituting this into the expression for m o size 12{m rSub { size 8{o} } } {} gives

m o = d i d o = 186 mm 6.20 mm = 30.0.

Now we must find the magnification of the eyepiece, which is given by

m e = d i d o , size 12{m rSub { size 8{e} } = - { {d rSub { size 8{i} } rSup { size 8{'} } } over {d rSub { size 8{o} } rSup { size 8{'} } } } } {}

where d i size 12{d rSub { size 8{i} rSup { size 8{'} } } } {} and d o size 12{d rSub { size 8{o} rSup { size 8{'} } } } {} are the image and object distances for the eyepiece (see [link] ). The object distance is the distance of the first image from the eyepiece. Since the first image is 186 mm to the right of the objective and the eyepiece is 230 mm to the right of the objective, the object distance is d o = 230 mm 186 mm = 44.0 mm . This places the first image closer to the eyepiece than its focal length, so that the eyepiece will form a case 2 image as shown in the figure. We still need to find the location of the final image d i in order to find the magnification. This is done as before to obtain a value for 1 / d i size 12{ {1} slash {d rSub { size 8{i} rSup { size 8{'} } } } } {} :

1 d i = 1 f e 1 d o = 1 50.0 mm 1 44.0 mm = 0.00273 mm . size 12{ { {1} over {d rSub { size 8{i} } rSup { size 8{'} } } } = { {1} over {f rSub { size 8{e} } } } - { {1} over {d rSub { size 8{o} } rSup { size 8{'} } } } = { {1} over {"50" "." "0 mm"} } - { {1} over {"44" "." "0 mm"} } = - { {0 "." "00273"} over {"mm"} } } {}

Inverting gives

d i = mm 0 . 00273 = 367 mm . size 12{d rSub { size 8{i} } rSup { size 8{'} } = - { {"mm"} over {0 "." "00273"} } = - "367 mm"} {}

The eyepiece’s magnification is thus

m e = d i d o = 367 mm 44 . 0 mm = 8 . 33 . size 12{m rSub { size 8{e} } = - { {d rSub { size 8{i} } rSup { size 8{'} } } over {d rSub { size 8{o} } rSup { size 8{'} } } } = - { { - "367 mm"} over {"44" "." "0 mm"} } =8 "." "33"} {}

So the overall magnification is

m = m o m e = ( 30.0 ) ( 8 . 33 ) = 250 . size 12{m=m rSub { size 8{o} } m rSub { size 8{e} } = \( - "30" "." 0 \) \( 8 "." "33" \) = - "250"} {}

Discussion

Both the objective and the eyepiece contribute to the overall magnification, which is large and negative, consistent with [link] , where the image is seen to be large and inverted. In this case, the image is virtual and inverted, which cannot happen for a single element (case 2 and case 3 images for single elements are virtual and upright). The final image is 367 mm (0.367 m) to the left of the eyepiece. Had the eyepiece been placed farther from the objective, it could have formed a case 1 image to the right. Such an image could be projected on a screen, but it would be behind the head of the person in the figure and not appropriate for direct viewing. The procedure used to solve this example is applicable in any multiple-element system. Each element is treated in turn, with each forming an image that becomes the object for the next element. The process is not more difficult than for single lenses or mirrors, only lengthier.

Questions & Answers

is economics important in programming world?
Abdul Reply
What is oppunity cost
Kudzanayi Reply
it refers wants that are left unsatisfied in Oder satisfy another more pressing need
Osei
Thank bro
Kudzanayi
is the second altenative to foregone
swedy
How does monopoly and imperfect competion;public goods externalities ass symmetric information, ommon property ressourses; income distribution Merit goods and Macroeconomic growth and stability causes market failure?
Gcina
it is where by a labour moves from one place to another
Amoako Reply
yh
Osei
another
Amoako
yh
Osei
ok
Amoako
what is mobility of labour
George Reply
who best defined economics
paul Reply
what are the importance of economics
Adwoa Reply
answer
Asamoah
trade should be best
Aakash
help to know how our government operates in which system
swedy
1. To solve economic problems. 2. To predict economic event. 3. It also offer intellectual training to students.
samuel
How price elasticity can affect the markets of certain goods
Rhoda Reply
Heyy thanks for the teaching
Easter Reply
what is labour
Arthur Reply
Mental and physical ability of human being is considered as labour.
JEYARAM
and usually provided by human
KEMAWOR
is all human effort both physical and mental abilities to work
Asamoah
why is it that most countries in Africa abuse available resources
Okeoghene Reply
What is economics
Bright Reply
economics is a science which studies human behaviour as a relationship between ends, scarce means which have alternative uses.
prince
Why is scarcity a mind problem in economics
Alima Reply
because of the problem of allocation of resources
Osola
unequalled distribution of resources
Agyen
thanks
Alima
scarcity is a mind problem due to circumstances like when a particular product is demand in a high rate at the market.
Saihou
scarcity defines limited in supply relative to the demand them. so scarcity is a mind problem in economics because wants are unlimited while resources are also limited.
prince
it is a mind problem because it's one of the fundamental issue address by economics human wants are unlimited and resources available are limited this makes the study of economics essential
rashid
its a fundamental issue
zahid
it's not a mind problem, I think it's a economic problem, how to allocate scarce resources to satisfy need and want of society
Samiullah
Identify the different sectors in the economy
Moses Reply
what is economics
Moses
economic is study of human behaviour according to how they satisfie their numerous want
Osola
Economics is a science which studies human behaviour as a relationship between ends and scares resources.
JEYARAM
economic is study of human behaviour according to how they satisfie their numerous want
Amar
what is the law of demand
Adugbire Reply
the lower the price the higher the quantity demanded vice versa is true
Nadhin
yes
vivek
yes ooh
Asamoah
right
samuel
what are relationship between unemployment and economic growth
Weness Reply
no relationship
Awuah
When there is economic growth, there is increased opportunity in employment. When there is no economic growth mean there is recession causing a decline or downsizing in employment opportunities.
Teescou
unemployment or employment determined by the level of economic growth
Osola
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 4

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Physics for the modern world. OpenStax CNX. Sep 16, 2015 Download for free at http://legacy.cnx.org/content/col11865/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for the modern world' conversation and receive update notifications?

Ask