Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 24, Problem 3P

(a)

To determine

The focal length of the second lens.

(a)

Expert Solution
Check Mark

Answer to Problem 3P

The focal length of the second lens is 11.8cm_.

Explanation of Solution

Given that the distance between the two converging lenses is 88.0cm, the distance between the first lens and the object is 1.100m, the focal length of the first lens is 25.0cm, the distance between the second lens and the final image is 15.0cm.

Write the thin lens formula for the first lens.

  1f1=1p1+1q1                                                                                                               (I)

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

Solve equation (I) for q1.

  1q1=1f11p1q1=f1p1p1f1                                                                                                              (II)

Write the thin lens formula for the second lens.

  1f2=1p2+1q2                                                                                                           (III)

Here, f2 is the focal length of the second lens, p2 is the distance between the object and the second lens, and q2 is the distance between the image and the second lens.

Solve equation (III) for f2.

  1f2=p2+q2p2q2f2=p2q2p2+q2                                                                                                            (IV)

Write the expression for the object distance for the second lens.

  p2=sq1                                                                                                                 (V)

Here, s is the distance of separation between the two lenses.

Use equation (II) in (IV).

  p2=sf1p1p1f1                                                                                                       (VI)

Conclusion:

Substitute 88.0cm for s, 25.0cm for f1, and 1.100m for p1 in equation (VI) to find p2.

  p2=88.0cm(25.0cm)(1.100m)1.100m25.0cm=88.0cm(25.0cm)(1.100m×100cm1m)(1.100m×100cm1m)25.0cm=55.6cm

Substitute 55.6cm for p2, and 15.0cm for q2 in equation (IV) to find f2.

  f2=(55.6cm)(15.0cm)(55.6cm)+(15.0cm)=11.8cm

Therefore, the focal length of the second lens is 11.8cm_.

(b)

To determine

The total magnification of the system of the two lenses.

(b)

Expert Solution
Check Mark

Answer to Problem 3P

The total magnification of the system of the two lenses is 0.0793_.

Explanation of Solution

Given that the distance between the first lens and the object is 1.100m, the distance between the second lens and the final image is 15.0cm. It is obtained that the distance between the second lens and the its object is 55.6cm.

Write the expression for the magnification of the two lens.

  m1=q1p1

  m2=q2p2

Here, m1 is the magnification of the first lens, and m2 is the magnification of the second lens.

Write the expression for the magnification of the system of two lenses.

  m=m1m2                                                                                                               (VII)

Here, m is the total magnification.

Use the expressions for m1 and m2 in equation (VII).

  m=(q1p1)(q2p2)=q1q2p1p2                                                                                               (VIII)

The distance between the first lens and its image is given by the equation (II).

  q1=f1p1p1f1

Conclusion:

Substitute 25.0cm for f1, and 1.100m for p1 in equation (II) to find q1.

  q1=(25.0cm)(1.100m)(1.100m)(25.0cm)=(25.0cm)(1.100m×100cm1m)(1.100m×100cm1m)(25.0cm)=32.35cm

Substitute 1.100m for p1, 32.35cm for q1, 55.6cm for p2, and 15.0cm for q2 in equation (VIII) to find m.

  m=(32.35cm)(15.0cm)(1.100m)(55.6cm)=(32.35cm)(15.0cm)(1.100m×100cm1m)(55.6cm)=0.0793

Therefore, the total magnification of the system of the two lenses is 0.0793_.

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Chapter 24 Solutions

Physics

Ch. 24.5 - Prob. 24.7PPCh. 24.6 - Prob. 24.6CPCh. 24.6 - Prob. 24.8PPCh. 24 - Prob. 1CQCh. 24 - Prob. 2CQCh. 24 - Prob. 3CQCh. 24 - Prob. 4CQCh. 24 - Prob. 5CQCh. 24 - Prob. 6CQCh. 24 - Prob. 7CQCh. 24 - Prob. 8CQCh. 24 - Prob. 9CQCh. 24 - 10. For human eyes, about 70% of the refraction...Ch. 24 - Prob. 11CQCh. 24 - Prob. 12CQCh. 24 - Prob. 13CQCh. 24 - Prob. 14CQCh. 24 - Prob. 15CQCh. 24 - Prob. 16CQCh. 24 - Prob. 17CQCh. 24 - Prob. 18CQCh. 24 - Prob. 19CQCh. 24 - Prob. 1MCQCh. 24 - Prob. 2MCQCh. 24 - Prob. 3MCQCh. 24 - Prob. 4MCQCh. 24 - Prob. 5MCQCh. 24 - Prob. 6MCQCh. 24 - Prob. 7MCQCh. 24 - Prob. 8MCQCh. 24 - Prob. 9MCQCh. 24 - Prob. 10MCQCh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6PCh. 24 - Prob. 7PCh. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10PCh. 24 - Prob. 11PCh. 24 - Prob. 12PCh. 24 - Prob. 13PCh. 24 - Prob. 14PCh. 24 - Prob. 15PCh. 24 - Prob. 16PCh. 24 - Prob. 17PCh. 24 - Prob. 18PCh. 24 - Prob. 19PCh. 24 - Prob. 20PCh. 24 - Prob. 21PCh. 24 - Prob. 22PCh. 24 - Prob. 23PCh. 24 - Prob. 24PCh. 24 - Prob. 25PCh. 24 - Prob. 26PCh. 24 - Prob. 27PCh. 24 - Prob. 28PCh. 24 - Prob. 29PCh. 24 - Prob. 30PCh. 24 - 31. Suppose the distance from the lens to the...Ch. 24 - 32. ✦ Veronique is nearsighted; she cannot see...Ch. 24 - Prob. 33PCh. 24 - Prob. 35PCh. 24 - Prob. 37PCh. 24 - Prob. 36PCh. 24 - Prob. 38PCh. 24 - Prob. 34PCh. 24 - Prob. 39PCh. 24 - Prob. 40PCh. 24 - Prob. 41PCh. 24 - Prob. 42PCh. 24 - Prob. 43PCh. 24 - Prob. 44PCh. 24 - Prob. 45PCh. 24 - Prob. 46PCh. 24 - Prob. 47PCh. 24 - Prob. 48PCh. 24 - Prob. 49PCh. 24 - Prob. 50PCh. 24 - Prob. 51PCh. 24 - Prob. 52PCh. 24 - Prob. 53PCh. 24 - Prob. 54PCh. 24 - Prob. 55PCh. 24 - Prob. 56PCh. 24 - Prob. 57PCh. 24 - Prob. 58PCh. 24 - Prob. 59PCh. 24 - Prob. 61PCh. 24 - Prob. 60PCh. 24 - 62. ✦ The eyepiece of a Galilean telescope is a...Ch. 24 - Prob. 63PCh. 24 - Prob. 64PCh. 24 - Prob. 65PCh. 24 - Prob. 66PCh. 24 - Prob. 67PCh. 24 - Prob. 68PCh. 24 - Prob. 69PCh. 24 - Prob. 70PCh. 24 - Prob. 71PCh. 24 - Prob. 72PCh. 24 - Prob. 73PCh. 24 - Prob. 74PCh. 24 - Prob. 75PCh. 24 - Prob. 76PCh. 24 - Prob. 77PCh. 24 - Prob. 78PCh. 24 - Prob. 79PCh. 24 - Prob. 80PCh. 24 - Prob. 81PCh. 24 - Prob. 82PCh. 24 - Prob. 83PCh. 24 - Prob. 84PCh. 24 - Prob. 85PCh. 24 - 86. (a) What is the angular size of the Moon as...Ch. 24 - Prob. 86P
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