COLLEGE PHYSICS-ACHIEVE AC (1-TERM)
COLLEGE PHYSICS-ACHIEVE AC (1-TERM)
3rd Edition
ISBN: 9781319453916
Author: Freedman
Publisher: MAC HIGHER
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Chapter 24, Problem 90QAP
To determine

(a)

The final image due to the lens-mirror combination.

Expert Solution
Check Mark

Answer to Problem 90QAP

The image formed by the mirror is located 750cm front of the mirror.

Explanation of Solution

Given:

A small, Plano-concave lens fA=45cm

Radius of curvature +60m

Focal length of spherical mirror is equal to the radius of curvature divided in half

  fB=30cm

Formula used:

  1fA=1dO,A+1d1,A

Calculation:

  1fA=1dO,A+1d1,A

  1d1,A=1fA1dO,A1d1,A=dO,AfAfAdO,Ad1,A=fAdO,AdO,AfA

  d1,A=(45)(15)(15)(45)d1,A=67560d1,A=11.25cm

Image formed by the mirror:

The image formed by lens is located 11.25cm behind the lens,

  dO,B=11.25+20=31.25cm

  1dO,B+1d1,B=1fB1d1,B=1fB1dO,B1d1,B=dO,BfBfBdO,Bd1,B=fBdO,BdO,BfBd1,B=(30)(31.25)31.2530d1,B=750cm

Conclusion:

The image formed by the mirror is located 750cm front of the mirror.

To determine

(b)

Find out final image is the virtual or real.

Expert Solution
Check Mark

Answer to Problem 90QAP

The image is inverted mtotal<0.

Explanation of Solution

Given:

A small, Plano-concave lens fA=45cm

Radius of curvature +60m

Focal length of spherical mirror is equal to the radius of curvature divided in half

  fB=30cm

Formula used:

  mtotal=mAmB

Calculation:

Since d1,B>0, the image is real.

Total magnification:

  mtotal=mAmBmtotal=( d 1,A d O,A)( d 1,B d O,b)mtotal=(11.2515)(75031.25)mtotal=18

Conclusion:

The image is inverted mtotal<0.

To determine

(c)

Calculate the final image due to the new lens-mirror combination from repeating part (a) and (b) when concave mirror is replaced by a convex mirror of same radius.

Expert Solution
Check Mark

Answer to Problem 90QAP

  d1,B<0, the image created by the mirror is virtual.

The image is upright mtotal>0.

Explanation of Solution

Given:

A small, Plano-concave lens fA=45cm

Radius of curvature +60m

Convex mirror of same magnitude radius of curvature have focal length is:

  fB=30cm

Formula used:

  mtotal=mAmB

Calculation:

  1dO,B+1d1,B=1fB1d1,B=1fB1dO,B1d1,B=dO,BfBfBdO,Bd1,B=fBdO,BdO,BfBd1,B=(30)(31.25)31.25(30)d1,B=15.3cm

Since d1,B<0, the image created by the mirror is virtual.

Total magnification:

  mtotal=mAmBmtotal=( d 1,A d O,A)( d 1,B d O,b)mtotal=(11.2515)(15.331.25)mtotal=0.367

Conclusion:

  d1,B<0, the image created by the mirror is virtual.

The image is upright mtotal>0.

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Chapter 24 Solutions

COLLEGE PHYSICS-ACHIEVE AC (1-TERM)

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