Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 24, Problem 48P

(a)

To determine

The distance between the lenses.

(a)

Expert Solution
Check Mark

Answer to Problem 48P

The distance between the lenses is 19.3cm.

Explanation of Solution

Assume that the final image is appeared at infinity. This happens when image of the objective is formed at focal length of the eyepiece. Therefore, distance between the lenses is the sum of focal length of eyepiece and image distance of the objective.

Write the expression for the distance between the lenses.

  d=qo+pe                                                                                                                 (I)

Here, d is the distance between lenses and qo is the image distance for the eyepiece.

Conclusion:

In problem it is given that, focal length of eyepiece is 2.80cm and image distance of object is 16.5cm.

Substitute 2.80cm for pe and 16.5cm for qo in equation (I) to get d.

  d=16.5cm+2.80cm=19.3cm

Therefore, the distance between the lenses is 19.3cm.

(b)

To determine

The angular magnification.

(b)

Expert Solution
Check Mark

Answer to Problem 48P

The angular magnification of the microscope is 286.

Explanation of Solution

Write the angular magnification for the eyepiece.

  Me=Nfe                                                                                                           (II)

Here, Me is the angular magnification of eyepiece,N is the near point.

Write the expression for the transverse magnification.

  mo=Lfo                                                                                                         (III)

Here, L is the tube length of the microscope and f0 is the focal length of objective.

Write the expression for the tube length of microscope.

  L=q0f0

Substitute qofo for L in equation (III) to get mo.

  mo=qofofo

Write the expression for total magnification.

  Mtotal=moMe                                                                                                       (IV)

Substitute qofofo for mo and Nfe for Me in equation (IV) to get Mtotal.

  Mtotal=qofofo×Nfe                                                                                           (V)

Conclusion:

Substitute 16.5cm for qo, 5.00mm for fo, 25.0cm for N and 2.80cm for fe in equation (V) to get Mtotal.

  Mtotal=16.5cm(5.00mm×1cm100mm)5.00mm×1cm100mm×25.0cm2.80cm=286

Therefore, the angular magnification of the microscope is 286.

(c)

To determine

The distance at which the object should be placed.

(c)

Expert Solution
Check Mark

Answer to Problem 48P

The distance at which the object should be placed is 5.16mm.

Explanation of Solution

Write mirror equation of objective.

  1po+1qo=1fo

Rearrange above equation to get p0.

  p0=(1fo1qo)1                                                                                            (VI)

Conclusion:

Substitute 16.5cm for qo and 5.00mm for fo in equation (VI) to get p0.

  p0=(15.00mm116.5cm×10mm1cm)1=5.16mm

Therefore, the distance at which the object should be placed is 5.16mm.

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Chapter 24 Solutions

Physics

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