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Chapter 26, Problem 73P

(a)

To determine

Radius of the mirror.

(a)

Expert Solution
Check Mark

Answer to Problem 73P

The radius should be greater than or equal to 0.334m_.

Explanation of Solution

Write the equation for power

    P=IA        (I)

Here P is the power, I is the intensity and A is the area of the circular cross section.

Write the equation for area.

    A=πRa2        (II)

Here Ra is the radius of the circular area of the mirror.

Substitute (II) in (I) and rewrite in terms of Ra.

    P=IπRa2Ra=IπP        (III)

Conclusion:

Substitute 350W for P and 1000W/m2 for I in (III)

    Ra=(1000W/m2)π350W=0.334

The radius should be greater than or equal to 0.334m_.

(b)

To determine

Relationship between Ra and R.

(b)

Expert Solution
Check Mark

Answer to Problem 73P

The ratio of Ra and R is given by RaR=0.0255_.

Explanation of Solution

Write the mirror equation

  1f=1p+1q=2R        (IV)

Here f is the focal length, R is the radius of curvature, p is the object distance and q is the image distance.

Write the equation for magnification

    M=hh=qp        (V)

Here h is the image height, h is the object height, p is the object distance and q is the image distance.

Object distance is infinite.

Then,

        q=R2        (VI)

Rearrange (V) in terms of h and substitute for q.

    h=qph=R2(hp)        (VII)

Here hp is the angle that sun subtends. Substitute 0.533° for hp in (VII)

    h=R2(0.533°(πrad180°))=R2(9.3mrad)        (VIII)

Write the equation for intensity of the image

    I=Pπr2        (IX)

Substitute r=h2 in (IX))

    I=Pπ(h2)2        (X)

Substitute (III) and (VIII) in (X)

    I=4IπRa2π(R/2)2(9.3×103rad)2RaR=I(9.3×103rad)216I        (XI)

Conclusion:

Substitute  1000W/m2 for I and 120×103W/m2 for I in (XI)

    RaR=(120×103W/m2)(9.3×103rad)216(1000W/m2)=0.0255

The ratio of Ra and R is given by RaR=0.0255_.

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Chapter 26 Solutions

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

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