Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 24, Problem 81P

(a)

To determine

The position of the final image.

(a)

Expert Solution
Check Mark

Answer to Problem 81P

The position of the final image is 5.3 cm to the left of the converging lens.

Explanation of Solution

Write lens equation for converging lens.

  1p1+1q1=1f1

Here, p1 is the object distance of for converging lens, q1 is the image distance for converging lens and f1 is the focal length of converging lens.

Rearrange above equation to get q1.

  q1=(1f11p1)1                                                                                                        (I)

The image produced by the converging lens acts as object for the diverging lens.

Write the expression for diverging lens.

  p2=sq1                                                                                                   (II)

Here, p2 is the object distance for diverging lens and s is the distance between converging and diverging lens.

Write lens equation for diverging lens to get q2.

  1p2+1q2=1f2q2=(1f21p2)1                                                                                           (III)

Here, q2 is the image distance for diverging lens and f2 is the focal length of diverging lens.

Conclusion:

Given that focal length of converging lens is 5.500cm, object distance is 9.000cm and focal length of diverging lens is 4.20cm.

Substitute 5.500cm for f1 and 9.000cm for p1 in equation (I) to get q1.

  q1=(15.500cm19.000cm)1=14.14cm

Substitute 8.00cm for s and 14.14cm for q1 in equation (II) to get p2.

  p2=8.00cm14.14cm=6.14cm

The negative sign for p2 indicates that the image is virtual.

Substitute 4.20cm for f2 and 6.14cm for p2 in equation (III) to get q2.

  q2=(14.20cm16.14cm)1=13.3cm

Since both the lenses are separated by 8.00cm, final image is formed at 13.3cm8.00cm=5.3cm to the left of the converging lens.

Therefore, the final image is formed at 5.3 cm to the left of the converging lens.

(b)

To determine

The height of the final image.

(b)

Expert Solution
Check Mark

Answer to Problem 81P

The height of the final image is 3.4cm.

Explanation of Solution

Write the expression for the magnification of image.

  m=qp

Here,m is the magnification, p is the object distance and q is the image distance.

Analogues to above equation, write magnification of the image formed by converging and diverging lens.

  m1=q1p1                                                                                                              (IV)

  m2=q2p2                                                                                                               (V)

Here,m1 is the magnification of the image formed by converging lens and m2 is the magnification of the image formed by diverging lens.

Write the expression for the total magnification.

  m=m1×m2

Substitute (IV) and (V) in above equation.

  m=q1p1(q2p2)                                                                                                     (VI)

Write magnification equation in terms of height of object and image.

  m=hh                                                                                                                   (VII)

Here, h is the height of image and h is the height of object.

Equate Equations (VI) and (VII) to get h.

  h=q1p1(q2p2)h                                                                                                     (VIII)

Conclusion:

Substitute 14.14cm for q1, 13.3cm for q2, 9.000cm for p1, 1.0cm for h and 6.14cm for p2 in (VIII) to get h

  h=14.14cm9.000cm(13.3cm6.14cm)(1.0cm)=3.4cm

Therefore, the height of the final image is 3.4cm.

(c)

To determine

Whether the image is upright or inverted.

(c)

Expert Solution
Check Mark

Answer to Problem 81P

The image is upright, since transverse magnification is positive.

Explanation of Solution

According to sign convention heights above principle axis are positive whereas heights below principle axis are negative.

In the question, since object is real upright h is positive. Since transverse magnification is positive, height of image should be positive. Therefore, image is upright.

Conclusion:

It is found that transverse magnification of the image is positive. This clearly indicates that the image is upright.

The image is upright, since transverse magnification is positive.

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Chapter 24 Solutions

Physics

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