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Chapter 2: Problem 11

Can an image be larger than the object even though its magnification is negative? Explain.

Short Answer

Expert verified
Yes, an image can be larger than the object even though its magnification is negative. The negativity of the magnification only indicates the orientation (inverted) of the image and does not limit the possibility of the image being larger than the object. The inequality \(I > -O\) verifies the situation where an image can be larger than the object with a negative magnification.

Step by step solution

01

Define magnification

Magnification (m) is defined as the ratio of the size of the image (I) to the size of the object (O), which can be written as: \( m = \frac{I}{O} \) A negative magnification indicates that the image is inverted or opposite in orientation as compared to the object.
02

Explore the possibilities of the magnification being negative

A negative magnification means the image is inverted in comparison to the object's orientation. The equation for magnification, \( m = \frac{I}{O} \), tells us that when magnification is negative: \( m = -\frac{I}{O} \) The sign of m only refers to the orientation of the image, but it doesn't say much about the size of the image. To find out if the image can be larger than the object, let's consider the following inequality: \( -\frac{I}{O} > 1 \)
03

Rearrange the inequality and isolate the image size

To determine if an image can be larger than the object, we need to check if the inequality above is true. If it is true, that means that the magnification is negative, but the image is still larger than the object. Solving the inequality, we isolate the image size (I) and make the object size (O) a constant: \( I > -O \) Since the object size is a positive value (O > 0), the negativity of the magnification doesn't automatically prohibit the image from being larger than the object.
04

Conclusion

Based on our analysis, an image can indeed be larger than the object even though its magnification is negative. The negativity of the magnification only indicates the orientation of the image and does not limit the possibility of the image being larger than the object.

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