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The magnification produced with a converging lens is 5. If the object is a square...

Physics
WAEC 1997

The magnification produced with a converging lens is 5. If the object is a square wire gauze of side 2cm, calculate the area of the image

  • A. 100\(cm^2\)
  • B. 40\(cm^2\)
  • C. 20\(cm^2\)
  • D. 10\(cm^2\)
  • E. 4\(cm^3\)
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Correct Answer: Option A
Explanation

To calculate the area of the image produced by a converging lens, we can use the magnification formula:

\(\text{Magnification} \, (M) = \frac{\text{Height of image}}{\text{Height of object}}\)

Given that the magnification \( M = 5 \) and the side of the square wire gauze (the object) is \( 2 \, \text{cm} \), we can find the height of the image:

\(\text{Height of image} = M \times \text{Height of object} = 5 \times 2 \, \text{cm} = 10 \, \text{cm}\)

Since the object is a square, the area of the object is:

\(\text{Area of object} = \text{side}^2 = (2 \, \text{cm})^2 = 4 \, \text{cm}^2\)

The area of the image can be calculated using the square of the magnification:

\(\text{Area of image} = M^2 \times \text{Area of object} = 5^2 \times 4 \, \text{cm}^2 = 25 \times 4 \, \text{cm}^2 = 100 \, \text{cm}^2\)

Thus, the area of the image is: 100cm\(^2\)


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