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Chapter 34: Q140P (page 1046)

Suppose the farthest distance a person can see without visual aid is50cm. (a) What is the focal length of the corrective lens that will allow the person to see very far away? (b) Is the lens converging or diverging? (c) The power Pof a lens (in diopters) is equal to1/f, wherefis in meters. What ispfor the lens?

Short Answer

Expert verified
  1. Focal length of the corrective lensf=-0.50cm
  2. The lens is diverging
  3. Power of the lensP=-2.0diopters

Step by step solution

01

Listing the given quantities

Far point of the personi=50cm

02

Understanding the concepts of lens formula and focal length

We will use the lens formula to find the focal length of the lens. The reciprocal of the focal length gives the power of the lens. If the focal length of the lens is negative, it is a diverging lens

Formula:

1f=1p+1i

Power of the lens,

role="math" localid="1663046890549" 1f=p

03

Calculations of the focal length of the corrective lens

(a)

Let鈥檚 take the object distance to be at infinity, i.e.,p=鈭�.

The image is inverted, therefore,theni=-0.50m

1f=1p+1i=1鈭�+1-0.50

Hence, the focal length of the lens isf=-0.50m

04

Type of the lens

(b)

As f<0, therefore the lens is diverging.

05

Calculations of the power of the lens

(c)

The power of the lens is defined as

P=1f=1-0.50=-2.0diopters

Power of the lensrole="math" localid="1663047184088" P=-2.0diopters

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Most popular questions from this chapter

An object is placed against the center of a thin lens and then moved away from it along the central axis as the image distance is measured. Figure 34-41 gives i versus object distance p out to ps=60cm. What is the image distancewhen p=100cm?


Isaac Newton, having convinced himself (erroneously as it turned out) that chromatic aberration is an inherent property of refracting telescopes, invented the reflecting telescope, shown schematically in Fig. 34-59. He presented his second model of this telescope, with a magnifying power of 38, to the Royal Society (of London), which still has it. In Fig. 34-59, incident light falls, closely parallel to the telescope axis, on the objective mirror. After reflection from the small mirror (the figure is not to scale), the rays form a real, inverted image in the focal plane (the plane perpendicular to the line of sight, at focal point F). This image is then viewed through an eyepiece. (a) Show that the angular magnification for the device is given by Eq. 34-15:

m胃=fob/fey

fob

the focal length of the objective is a mirror and

feyis that of the eyepiece.

(b) The 200 in. mirror in the reflecting telescope at Mt. Palomar in California has a focal length of 16.8 m. Estimate the size of the image formed by this mirror when the object is a meter stick 2.0 km away. Assume parallel incident rays. (c) The mirror of a different reflecting astronomical telescope has an effective radius of curvature of 10 m (鈥渆ffective鈥� because such mirrors are ground to a parabolic rather than a spherical shape, to eliminate spherical aberration defects). To give an angular magnification of 200, what must be the focal length of the eyepiece?

17 through 29 22 23, 29 More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation, each problem in Table 34-4 refers to (a) the type of mirror, (b) the focal distance f, (c) the radius of curvature r, (d) the object distance p, (e) the imagedistance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R)or virtual localid="1662996882725" (V), (h) inverted (I)or noninverted (NI)from O, and (i) on the same side of the mirror as object O or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

A narrow beam of parallel light rays is incident on a glass sphere from the left, directed toward the center of the sphere. (The sphere is a lens but certainly not a thin lens.) Approximate the angle of incidence of the rays as 0掳, and assume that the index of refraction of the glass is n<2.0(a) In terms of n and the sphere radius r, what is the distance between the image produced by the sphere and the right side of the sphere? (b) Is the image to the left or right of that side? (Hint: Apply Eq. 34-8 to locate the image that is produced by refraction at the left side of the sphere; then use that image as the object for refraction at the right side of the sphere to locate the final image. In the second refraction, is the object distance positive or negative?)

Prove that if a plane mirror is rotated through an angle a, the reflected beam is rotated through an angle 2伪. Show that this result is reasonable for 伪=45鈭�.
See all solutions

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