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Chapter 26, Problem 54P

(a)

To determine

The equation relating the focal length f of the lens to the object distance p1 .

(a)

Expert Solution
Check Mark

Answer to Problem 54P

The equation relating the focal length f of the lens to the object distance p1 is 1f=1p1+11.50mp1 .

Explanation of Solution

Given info: The distance between the candle and the wall is 1.50m . The distance by which the lens is moved is 90.0cm . The focal length of the lens is f , the object distance is p1 .

Write the expression of lens equation.

1f=1p1+1q1 (1)

Here,

q1 is the distance of image from the lens.

The sum of image and object distance is,

p1+q1=1.50mq1=1.50mp1

Substitute 1.50mp1 for q1 in equation (1).

1f=1p1+11.50mp1 . (2)

Conclusion:

Therefore, the equation relating the focal length f of the lens to the object distance p1 is 1f=1p1+11.50mp1 .

(b)

To determine

The equation relating the focal length f of the lens to the object distance p1 .

(b)

Expert Solution
Check Mark

Answer to Problem 54P

The equation relating the focal length f of the lens to the object distance p1 is 1f=1p1+0.900m+10.600mp1 .

Explanation of Solution

Given info: The distance between the candle and the wall is 1.50m . The distance by which the lens is moved is 90.0cm . The focal length of the lens is f , the object distance is p1 .

Write the expression of lens equation.

1f=1p2+1q2 (3)

Here,

p2 is the final object distance.

q2 is the final image distance.

The final distance of object is,

p2=p1+90cm×102m1cm=p1+0.900m

The final distance of image is,

q2=q190cm×102m1cm=q10.900m

Substitute 1.50mp1 for q1 in above equation.

q2=1.50mp10.900m=0.600mp1

Substitute 0.600mp1 for q2 and p1+0.900m for p2 in equation (3).

1f=1p1+0.900m+10.600mp1 (4)

Thus, the equation relating the focal length f of the lens to the object distance p1 is 1f=1p1+0.900m+10.600mp1 .

Conclusion:

Therefore, the equation relating the focal length f of the lens to the object distance p1 is 1f=1p1+0.900m+10.600mp1 .

(c)

To determine

The value of p1 .

(c)

Expert Solution
Check Mark

Answer to Problem 54P

The value of p1 is 0.30m .

Explanation of Solution

Given info: The distance between the candle and the wall is 1.50m . The distance by which the lens is moved is 90.0cm . The focal length of the lens is f , the object distance is p1 .

Compare equation (2) and (4).

1p1+11.50mp1=1p1+0.900m+10.600mp11.50mp1+p2p1(1.50mp1)=0.600mp1+p1+0.900m(p1+0.900m)(0.600mp1)p1(1.50mp1)=(p1+0.900m)(0.600mp1)p1=0.30m

Conclusion:

Therefore, the value of p1 is 0.30m .

(d)

To determine

The focal length of the lens.

(d)

Expert Solution
Check Mark

Answer to Problem 54P

The focal length of the lens is 0.240m .

Explanation of Solution

Given info: The distance between the candle and the wall is 1.50m . The distance by which the lens is moved is 90.0cm . The focal length of the lens is f , the object distance is p1 .

The equation relating the focal length f of the lens to the object distance p1 is,

1f=1p1+11.50mp1

Substitute 0.30m for p1 in above equation.

1f=10.30m+11.50m0.30mf=0.240m

Thus, the focal length of the lens is 0.240m .

Conclusion:

Therefore, the focal length of the lens is 0.240m .

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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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