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All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be larger than the object. (b) Makeup mirrors are perhaps the most common use of a concave mirror to produce a larger, upright image.

A convex mirror is a diverging mirror ( f size 12{f} {} is negative) and forms only one type of image. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses. [link] (a) uses ray tracing to illustrate the location and size of the case 3 image for mirrors. Since the image is behind the mirror, it cannot be projected and is thus a virtual image. It is also seen to be smaller than the object.

Figure (a) shows three incident rays, 1, 2, and 3, falling on a convex mirror. Ray 1 falls parallel, ray 2 falls making an angle with the axis, and ray 3 falls obliquely. These rays after reflection appear to come from a point above the axis. The image is erect and diminished and falls above the axis behind the mirror. Here, the distance from the center of the mirror to focal point F is the focal length small f behind the mirror; the 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. Figure (b) shows an image of a apparel and clothing show room as viewed in a convex mirror; the image appears to be small in size.
Case 3 images for mirrors are formed by any convex mirror. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches toward the focal point. All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be smaller than the object. (b) Security mirrors are convex, producing a smaller, upright image. Because the image is smaller, a larger area is imaged compared to what would be observed for a flat mirror (and hence security is improved). (credit: Laura D’Alessandro, Flickr)

Image in a convex mirror

A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is 12.0 cm from the cornea and the image’s magnification is 0.0320, what is the cornea’s radius of curvature?

Strategy

If we can find the focal length of the convex mirror formed by the cornea, we can find its radius of curvature (the radius of curvature is twice the focal length of a spherical mirror). We are given that the object distance is d o = 12.0 cm and that m = 0.0320 . We first solve for the image distance d i , and then for f size 12{f} {} .

Solution

m = –d i / d o . Solving this expression for d i gives

d i = md o .

Entering known values yields

d i = 0 . 0320 12.0 cm = –0.384 cm. size 12{d rSub { size 8{i} } "=-" left (0 "." "0320" right ) left ("12" "." 0" cm" right )"=-"0 "." "384"" cm"} {}
1 f = 1 d o + 1 d i size 12{ { {1} over {f} } = { {1} over {d rSub { size 8{o} } } } + { {1} over {d rSub { size 8{i} } } } } {}

Substituting known values,

1 f = 1 12.0 cm + 1 0 . 384 cm = 2 . 52 cm . size 12{ { {1} over {f} } = { {1} over {"12" "." 0" cm"} } + { {1} over {-0 "." "384"" cm"} } = { {-2 "." "52"} over {"cm"} } } {}

This must be inverted to find f size 12{f} {} :

f = cm 2 . 52 = –0 . 400 cm . size 12{f= { {"cm"} over { +- 2 "." "52"} } "=-"0 "." "400"" cm"} {}

The radius of curvature is twice the focal length, so that

R = 2 f = 0 . 800 cm. size 12{R=2 lline f rline =0 "." "800"" cm"} {}

Discussion

Although the focal length f size 12{f} {} of a convex mirror is defined to be negative, we take the absolute value to give us a positive value for R size 12{R} {} . The radius of curvature found here is reasonable for a cornea. The distance from cornea to retina in an adult eye is about 2.0 cm. In practice, many corneas are not spherical, complicating the job of fitting contact lenses. Note that the image distance here is negative, consistent with the fact that the image is behind the mirror, where it cannot be projected. In this section’s Problems and Exercises, you will show that for a fixed object distance, the smaller the radius of curvature, the smaller the magnification.

Questions & Answers

a 50kg mass is placed on a frictionless piston fitted to a gas cylinder .If 149 kelvin of heat is supplied to the cylinder increasing the internal energy by 100 joules,determine the height through which the mass of the piston raise
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thermodynamic is a branch of physics that teaches on the relationship about heat and anyother form of energy
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Lawal
if a mass of 149 of heat is supplied and there's an increase in internal energy of 100jouls,find the raise in height
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fundamental unit are independent quantities that do not depend on any other unit while derived unit are quantities that depend on two or more units for it definition
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vector is any quantity that has magnitude and direction
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physics is a physical science that deals with the study of matter in relation to energy
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movement in a direction
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Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
anas Reply
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An object made of several thin conducting layers separated by insulation may not be affected by magnetic damping because the eddy current produced in each layer due to induction will be very small and the opposing magnetic flux produced by the eddy currents will be very small
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Force×perpendicular distance N×m=Nm
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It is difficult to have an ideal machine in real life situation because in ideal machines all the input energy should be converted to output energy . But , some part of energy is always lost in overcoming friction and input energy is always greater than output energy . Hence , no machine is ideal.
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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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