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An illuminated slide is held 44cm from a screen. How far from the slide must a lens of focal length11cm be placed (between the slide and the screen) to form an image of the slide’s picture on the screen?

Short Answer

Expert verified

Distance from the slide at which the lens should be placed is 22cm.

Step by step solution

01

Listing the given quantities

Focal length,f=11cm.

Distance between slide and screen is 44cm

02

Understanding the concepts of lens equation

By using the thin lens equation, we can find the distance at which the lens should be placed.

Formula:

Thin lens equation,

1f=1p+1i

03

Calculations of the distance from the slide at which the lens should be placed

Thin lens equationis

1f=1p+1i

Since the image is formed on the screen, so the sum of the object distance and the image distance is equal to the distance between the slide and the screen.

As the distance between slide and screen is44cm, i.e.

p+i=44cmOr

i=44−p

Therefore,

111=1p+144−p111=(44−p)+p44p−p2111=4444p−p2

44p−p2=484

p2−44p+484=0

After solving the quadratic equation, we get,

p=22cm

Distance from the slide at which the lens should be placed is 22cm

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Most popular questions from this chapter

In Fig. 34-26, stick figure O stands in front of a thin, symmetric lens that is mounted within the boxed region; the central axis through the lens is shown. The four stick figuresI1andI4suggest general locations and orientations for the images that might be produced by the lens. (The figures are only sketched in; neither their height nor their distance from the lens is drawn to scale.) (a) Which of the stick figures could not possibly represent images? Of the possible images, (b) which would be due to a converging lens, (c) which would be due to a diverging lens, (d) which would be virtual, and (e) which would involve negative magnification?

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?

58 through 67 61 59 Lenses with given radii. An object Ostands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius r1of the nearer lens surface, and radius r2of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R)or virtual (V), (d) inverted (I)from the object Oor non-inverted (NI), and (e) on the same side of the lens as object Oor on the opposite side

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.

Figure 34-37 gives the lateral magnification mof an object versus the object distanc pfrom a spherical mirror as the object is moved along the mirror’s central axis through a range of values p. The horizontal scale is set by Ps=10.0mm. What is the magnification of the object when the object is 21cm from the mirror?

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