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Although a spherical mirror is shown in part (b) of [link] , comatic aberration occurs also for parabolic mirrors—it does not result from a breakdown in the small-angle approximation. Spherical aberration, however, occurs only for spherical mirrors and is a result of a breakdown in the small-angle approximation. We will discuss both coma    and spherical aberration later in this chapter, in connection with telescopes.

Summary

  • Spherical mirrors may be concave (converging) or convex (diverging).
  • The focal length of a spherical mirror is one-half of its radius of curvature: f = R / 2 .
  • The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror.
  • Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors.

Conceptual questions

At what distance is an image always located: at d o , d i , or f ?

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Under what circumstances will an image be located at the focal point of a spherical lens or mirror?

when the object is at infinity; see the mirror equation

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What is meant by a negative magnification? What is meant by a magnification whose absolute value is less than one?

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Can an image be larger than the object even though its magnification is negative? Explain.

Yes, negative magnification simply means that the image is upside down; this does not prevent the image from being larger than the object. For instance, for a concave mirror, if distance to the object is larger than one focal distance but smaller than two focal distances the image will be inverted and magnified.

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Problems

The following figure shows a light bulb between two spherical mirrors. One mirror produces a beam of light with parallel rays; the other keeps light from escaping without being put into the beam. Where is the filament of the light in relation to the focal point or radius of curvature of each mirror?

A light bulb is shown in the centre, with a small concave mirror to its left and a bigger one to its right. The light rays originating from the bulb that hit the smaller mirror are reflected back to the bulb. Light rays from the bulb that hit the bigger mirror are reflected. These reflected rays are parallel and travel towards the left.

It is in the focal point of the big mirror and at the center of curvature of the small mirror.

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Why are diverging mirrors often used for rearview mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?

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Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm-focal length telephoto lens?

f = R 2 R = + 1.60 m

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Calculate the focal length of a mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature.

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Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR radiation 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?

d o = 27.3 cm

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Find the magnification of the heater element in the previous problem. Note that its large magnitude helps spread out the reflected energy.

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What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the [link] .

Step 1: Image formation by a mirror is involved.
Step 2: Draw the problem set up when possible.
Step 3: Use thin-lens equations to solve this problem.
Step 4: Find f.
Step 5: Given: m = 1.50 , d o = 0.120 m .
Step 6: No ray tracing is needed.
Step 7: Using m = d i d o , d i = −0.180 m . Then, f = 0.360 m .
Step 8: The image is virtual because the image distance is negative. The focal length is positive, so the mirror is concave.

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A shopper standing 3.00 m from a convex security mirror sees his image with a magnification of 0.250. (a) Where is his image? (b) What is the focal length of the mirror? (c) What is its radius of curvature?

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An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.167 cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by optometrists to measure the curvature of the cornea for contact lens fitting. The instrument used is called a keratometer, or curve measurer.)

a. for a convex mirror d i < 0 m > 0 . m = + 0.111 ; b. d i = −0.334 cm (behind the cornea);
c. f = −0.376 cm, so that R = −0.752 cm

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Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. This is stated as d i = d o , since this is a negative image distance (it is a virtual image). What is the focal length of a flat mirror?

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Show that, for a flat mirror, h i = h o , given that the image is the same distance behind the mirror as the distance of the object from the mirror.

m = h i h o = d i d o = d o d o = d o d o = 1 h i = h o

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Use the law of reflection to prove that the focal length of a mirror is half its radius of curvature. That is, prove that f = R / 2 . Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.

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Referring to the electric room heater considered in problem 5, calculate the intensity of IR radiation in W/m 2 projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 W and has an area of 100 cm 2 , and that half of the radiated power is reflected and focused by the mirror.

Figure shows the cross section of a concave mirror. Two rays originating from a point strike the mirror and are reflected. The distance of the point from the mirror is labeled d subscript o = 0.273 m and d subscript i = 3.00 m.
m = −11.0 A = 0.110 m 2 I = 6.82 kW/m 2

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Two mirrors are inclined at an angle of 60 ° and an object is placed at a point that is equidistant from the two mirrors. Use a protractor to draw rays accurately and locate all images. You may have to draw several figures so that that rays for different images do not clutter your drawing.

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Two parallel mirrors are facing each other and are separated by a distance of 3 cm. A point object is placed between the mirrors 1 cm from one of the mirrors. Find the coordinates of all the images.

x 2 m = x 2 m 1 , ( m = 1 , 2 , 3 , ... ) , x 2 m + 1 = b x 2 m , ( m = 0 , 1 , 2 , ... ) , with x 0 = a .

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Questions & Answers

why we have physics
Anil Reply
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
is this a physics forum
Physics Reply
explain l-s coupling
Depk Reply
how can we say dirac equation is also called a relativistic equation in one word
preeti Reply
what is the electronic configration of Al
usman Reply
what's the signeficance of dirac equetion.?
Sibghat Reply
what is the effect of heat on refractive index
Nepal Reply
As refractive index depend on other factors also but if we supply heat on any system or media its refractive index decrease. i.e. it is inversely proportional to the heat.
ganesh
you are correct
Priyojit
law of multiple
Wahid
if we heated the ice then the refractive index be change from natural water
Nepal
can someone explain normalization condition
Priyojit Reply
please tell
Swati
yes
Chemist
1 millimeter is How many metres
Darling Reply
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material. 
Chris Reply
What is photoelectric effect
Amit Reply
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
Laxmikanta Reply
why does not electron exits in nucleaus
Kabbo Reply
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
BARISUA Reply

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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