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Three incident rays, 1, 2, and 3, falling on a concave mirror. Ray 1 falls parallel, ray 2 falls making an angle with the axis and ray 3 passes through focal point F. These rays after reflection converge at a point below the axis. The image is inverted and enlarged and falls below the axis on the same side as the object. Here, the distance from the center of the mirror to F is the focal distance small f, distances of the object and the image from the mirror are d sub o and d sub I, respectively. The heights of the object and the image are h sub o and h sub I, respectively.
A case 1 image for a mirror. An object is farther from the converging mirror than its focal length. Rays from a common point on the object are traced using the rules in the text. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 goes through the focal point on the way toward the mirror. All three rays cross at the same point after being reflected, locating the inverted real image. Although three rays are shown, only two of the three are needed to locate the image and determine its height.

A concave reflector

Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m away from the mirror, where are the coils?

Strategy and Concept

We are given that the concave mirror projects a real image of the coils at an image distance d i = 3.00 m . The coils are the object, and we are asked to find their location—that is, to find the object distance d o . We are also given the radius of curvature of the mirror, so that its focal length is f = R / 2 = 25.0 cm (positive since the mirror is concave or converging). Assuming the mirror is small compared with its radius of curvature, we can use the thin lens equations, to solve this problem.

Solution

Since d i size 12{d rSub { size 8{i} } } {} and f size 12{f} {} are known, thin lens equation can be used to find d o size 12{d rSub { size 8{o} } } {} :

1 d o + 1 d i = 1 f . size 12{ { {1} over {d rSub { size 8{o} } } } + { {1} over {d rSub { size 8{i} } } } = { {1} over {f} } } {}

Rearranging to isolate d o size 12{d rSub { size 8{o} } } {} gives

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

Entering known quantities gives a value for 1/ d o size 12{d rSub { size 8{o} } } {} :

1 d o = 1 0 . 250 m 1 3 . 00 m = 3 . 667 m . size 12{ { {1} over {d rSub { size 8{o} } } } = { {1} over {0 "." "250"" m"} } - { {1} over {3 "." "00"" m"} } = { {3 "." "667"} over {m} } } {}

This must be inverted to find d o size 12{d rSub { size 8{o} } } {} :

d o = 1 m 3 . 667 = 27 . 3 cm. size 12{d rSub { size 8{o} } = { {"1 m"} over {3 "." "667"} } ="27" "." 3" cm"} {}

Discussion

Note that the object (the filament) is farther from the mirror than the mirror’s focal length. This is a case 1 image ( d o > f and f positive), consistent with the fact that a real image is formed. You will get the most concentrated thermal energy directly in front of the mirror and 3.00 m away from it. Generally, this is not desirable, since it could cause burns. Usually, you want the rays to emerge parallel, and this is accomplished by having the filament at the focal point of the mirror.

Note that the filament here is not much farther from the mirror than its focal length and that the image produced is considerably farther away. This is exactly analogous to a slide projector. Placing a slide only slightly farther away from the projector lens than its focal length produces an image significantly farther away. As the object gets closer to the focal distance, the image gets farther away. In fact, as the object distance approaches the focal length, the image distance approaches infinity and the rays are sent out parallel to one another.

Solar electric generating system

One of the solar technologies used today for generating electricity is a device (called a parabolic trough or concentrating collector) that concentrates the sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where its heat energy is transferred to another system that is used to generate steam—and so generate electricity through a conventional steam cycle. [link] shows such a working system in southern California. Concave mirrors are used to concentrate the sunlight onto the pipe. The mirror has the approximate shape of a section of a cylinder. For the problem, assume that the mirror is exactly one-quarter of a full cylinder.

Questions & Answers

derivative of first differential equation
Haruna Reply
why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
what Is linear momentum
Victoria Reply
why no diagrams
Blessing Reply
where
Fayyaz
Myanmar
Pyae
hi
Iroko
hello
Abdu
Describe an experiment to determine short half life
Tyson Reply
what is science
Kenedy Reply
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
there are seven basic type of wave radio waves, gyamma rays (nuclear energy), microwave,etc you can also search 🔍 on Google :-)
Shravasti
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
what is physics
Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
Magret Reply
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
fundamental quantities are, length , mass, time, current, luminous intensity, amount of substance, thermodynamic temperature.
Shravasti
fundamental quantities are quantities that are independent of others and cannot be define in terms of other quantities there is nothing like Qualities we have only fundamental quantities which includes; length,mass,time, electric current, luminous density, temperature, amount of substance etc
Gift
give examples of three dimensional frame of reference
Ekwunazor Reply
Universe
Noman
Yes the Universe itself
Astronomy
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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