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69 through 79 76, 78 75, 77 More lenses. Objectstands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging or diverging , (b) the focal distance , (c) the object distance , (d) the image distance , and (e) the lateral magnification . (All distances are in centimetres.) It also refers to whether (f) the image is real or virtual , (g) inverted (I)or non-inverted(NI) from , and (h) on the same side of the lens asor on the opposite side. Fill in the missing information, including the value of m when only an inequality is given, where only a sign is missing, answer with the sign.

Short Answer

Expert verified
  1. The lens type is converging.
  2. The focal distance is+10cm.
  3. The object distance is5.0cm.
  4. The image distance is-10cm.
  5. The lateral magnification is +2.0.
  6. The image is virtual V.
  7. The image is non-invertedNI.
  8. The image is on the same side of the lens as the object.

Step by step solution

01

The given data

  1. Object distance,p=+5.0cm
  2. The focal length of the lens, f=+10cm
02

 Step 2: Understanding the concept of properties of the lens

Here, we need to use the concept of image formation by the thin lens. We can use equation 34.9 to solve for the image distance. The magnification of the lens can be calculated using equation 34.7. By using the values of image distance and magnification, and comparing the value of object distance and focal length we can determine whether the image is real or virtual, whether it is inverted or non-inverted, and whether it is on the same side as the object or on the opposite side.

03

 Step 3: Calculation of the lens type

(a)

The value of the focal length is positive.

Hence, the lens is a converging lens.

04

 Step 4: Calculation of the focal distance

(b)

From the given data, the value of focal length is given as:f=+10cm.

Hence, the focal distance is +10cm.

05

Calculation of the object distance

(c)

From the given data, the value of object distance is given as:p=+5.0cm

Hence, the object distance is +5.0cm.

06

Calculation of the image distance

(d)

Now, using the above data in equation (i), we can get the image distance as follows:

1i=110cm-15.0cm=-0.1cmi=-10cm

Hence, the image distance is -10cm.

07

 Step 7: Calculation of the lateral magnification

(e)

Using the given data in equation (ii), we can get the lateral magnification of the lens as follows:

m=--105.0=+2.0

Hence, the value of magnification is +2.0.

08

Calculation of the type of image

(f)

The value of image distance is negative.

Hence, the image is virtual (V).

09

 Step 9: Calculation if the image is inverted or not

(g)

The value of lateral magnification is positive.

Hence, the image is non-inverted (NI).

10

Calculation of the position of the object

(h)

From the above data, it is given thatp<f.

Hence, the image is on the same side as object.

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Most popular questions from this chapter

The equation 1p+1i=2rfor spherical mirrors is an approximation that is valid if the image is formed by rays that make only small angles with the central axis. In reality, many of the angles are large, which smears the image a little. You can determine how much. Refer to Fig. 34-22 and consider a ray that leaves a point source (the object) on the central axis and that makes an angle a with that axis. First, find the point of intersection of the ray with the mirror. If the coordinates of this intersection point are x and y and the origin is placed at the center of curvature, then y=(x+p-r)tan a and x2+ y2= r2where pis the object distance and r is the mirror鈥檚 radius of curvature. Next, use tan=yxto find the angle b at the point of intersection, and then use+y=2tofind the value of g. Finally, use the relationtany=y(x+i-r)to find the distance iof the image. (a) Suppose r=12cmand r=12cm. For each of the following values of a, find the position of the image 鈥 that is, the position of the point where the reflected ray crosses the central axis:(0.500,0.100,0.0100rad). Compare the results with those obtained with theequation1p+1i=2r.(b) Repeat the calculations for p=4.00cm.

32 through 38 37, 38 33, 35 Spherical refracting surfaces. An object Ostands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction n1where the object is located, (a) the index of refraction localid="1663039333438" n2on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature rof the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R)or virtual (V)and (f) on the same side of the surface as the object Oor on the opposite side.

The table details six variations of the basic arrangement of two thin lenses represented in Fig. 34-29. (The points labeledF1and F2are the focal points of lenses 1 and 2.) An object is distancep1to the left of lens 1, as in Fig. 34-18. (a) For which variations can we tell, without calculation, whether the final image (that due to lens 2) is to the left or right of lens 2 and whether it has the same orientation as the object? (b) For those 鈥渆asy鈥 variations, give the image location as 鈥渓eft鈥 or 鈥渞ight鈥 and the orientation as 鈥渟ame鈥 or 鈥渋nverted.鈥

A fruit fly of height H sits in front of lens 1 on the central axis through the lens. The lens forms an image of the fly at a distance d=20cmfrom the fly; the image has the fly鈥檚 orientation and height H1=2.0H. What are (a) the focal lengthf1 of the lens and (b) the object distance p1of the fly? The fly then leaves lens 1 and sits in front of lens 2, which also forms an image at d=20cmthat has the same orientation as the fly, but now H1=0.50H. What are (c) f2and (d) p2?

Figure 34-40 gives the lateral magnification of an object versus the object distancefrom a lens asthe object is moved along the central axis of the lens through a range of values for p out to ps=20.0cm. What is the magnification of the objectwhen the object is 35cmfrom the lens?

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