The Equation for Magnification

Oct 13, 2025 by pinkandtrash.com 121 views

Introduction

In optics, the magnification of an image formed by a mirror or a lens is a crucial concept that helps us understand how the size of the image is related to the size of the object. The magnification of an image is defined as the ratio of the height of the image to the height of the object. In this article, we will explore the concept of magnification and use the equation $m=-\frac{d_i}{d_0}$ to calculate the magnification of a real image formed by a mirror.

What is Magnification?

Magnification is a measure of how much an image is enlarged or reduced compared to the size of the object. It is a dimensionless quantity that can be either positive or negative. A positive magnification indicates that the image is enlarged, while a negative magnification indicates that the image is reduced.

The Equation for Magnification

The equation for magnification is given by:

m=-\frac{d_i}{d_0}

where $m$ is the magnification, $d_i$ is the distance between the image and the mirror, and $d_0$ is the distance between the object and the mirror.

Calculating the Magnification of a Real Image

To calculate the magnification of a real image, we need to know the distance between the image and the mirror ( $d_i$ ) and the distance between the object and the mirror ( $d_0$ ). In this example, we are given that the image is 10.0 cm from the mirror and the object is 50.0 cm from the mirror.

Using the equation $m=-\frac{d_i}{d_0}$ , we can plug in the values to get:

m=-\frac{10.0\text{ cm}}{50.0\text{ cm}}

Simplifying the equation, we get:

m=-0.20

Therefore, the magnification of the real image is -0.20.

Interpretation of the Results

The negative sign in the magnification indicates that the image is reduced compared to the size of the object. This is because the image is formed by a mirror, which is a convex mirror. Convex mirrors always produce reduced images.

Conclusion

In conclusion, the magnification of a real image formed by a mirror can be calculated using the equation $m=-\frac{d_i}{d_0}$ . By plugging in the values of the distance between the image and the mirror and the distance between the object and the mirror, we can determine the magnification of the image. In this example, we found that the magnification of the real image is -0.20.

Frequently Asked Questions

Q: What is the magnification of a real image formed by a mirror?

A: The magnification of a real image formed by a mirror can be calculated using the equation $m=-\frac{d_i}{d_0}$ .

Q: What is the distance between the image and the mirror?

A: The distance between the image and the mirror is given as 10.0 cm.

Q: What is the distance between the object and the mirror?

A: The distance between the object and the mirror is given as 50.0 cm.

Q: What is the magnification of the real image?

A: The magnification of the real image is -0.20.

Q: Why is the magnification negative?

A: The magnification is negative because the image is reduced compared to the size of the object. This is because the image is formed by a convex mirror, which always produces reduced images.

References

[1] Hecht, E. (2017). Optics (5th ed.). Pearson Education.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.

Glossary

Magnification: A measure of how much an image is enlarged or reduced compared to the size of the object.
Convex mirror: A type of mirror that is curved outward, which always produces reduced images.
Real image: An image that is formed by a mirror or a lens and is located at a distance from the mirror or lens.
Distance between the image and the mirror: The distance between the image and the mirror, which is given as 10.0 cm.
Distance between the object and the mirror: The distance between the object and the mirror, which is given as 50.0 cm.
Frequently Asked Questions: Magnification of a Real Image =====================================================

Q: What is the magnification of a real image formed by a mirror?

A: The magnification of a real image formed by a mirror can be calculated using the equation $m=-\frac{d_i}{d_0}$ .

Q: What is the distance between the image and the mirror?

A: The distance between the image and the mirror is given as 10.0 cm.

Q: What is the distance between the object and the mirror?

A: The distance between the object and the mirror is given as 50.0 cm.

Q: What is the magnification of the real image?

A: The magnification of the real image is -0.20.

Q: Why is the magnification negative?

A: The magnification is negative because the image is reduced compared to the size of the object. This is because the image is formed by a convex mirror, which always produces reduced images.

Q: What is the formula for calculating the magnification of a real image?

A: The formula for calculating the magnification of a real image is $m=-\frac{d_i}{d_0}$ , where $m$ is the magnification, $d_i$ is the distance between the image and the mirror, and $d_0$ is the distance between the object and the mirror.

Q: Can the magnification of a real image be positive?

A: No, the magnification of a real image cannot be positive. This is because the image is always reduced compared to the size of the object when formed by a convex mirror.

Q: What is the significance of the negative sign in the magnification?

A: The negative sign in the magnification indicates that the image is reduced compared to the size of the object. This is a characteristic of convex mirrors, which always produce reduced images.

Q: Can the magnification of a real image be zero?

A: No, the magnification of a real image cannot be zero. This is because the image is always formed at a distance from the mirror, and the magnification is a measure of how much the image is enlarged or reduced compared to the size of the object.

Q: How does the magnification of a real image change with the distance between the object and the mirror?

A: The magnification of a real image changes inversely with the distance between the object and the mirror. As the distance between the object and the mirror increases, the magnification of the image decreases.

Q: Can the magnification of a real image be affected by the type of mirror used?

A: Yes, the magnification of a real image can be affected by the type of mirror used. Convex mirrors always produce reduced images, while concave mirrors can produce enlarged or reduced images depending on the distance between the object and the mirror.

Q: What is the relationship between the magnification of a real image and the distance between the image and the mirror?

A: The magnification of a real image is inversely proportional to the distance between the image and the mirror. As the distance between the image and the mirror increases, the magnification of the image decreases.

Q: Can the magnification of a real image be affected by the size of the object?

A: Yes, the magnification of a real image can be affected by the size of the object. The magnification of the image is a measure of how much the image is enlarged or reduced compared to the size of the object.

Q: What is the significance of the magnification of a real image in optics?

A: The magnification of a real image is a fundamental concept in optics that helps us understand how images are formed by mirrors and lenses. It is a measure of how much an image is enlarged or reduced compared to the size of the object.

Q: Can the magnification of a real image be used to calculate the distance between the object and the mirror?

A: Yes, the magnification of a real image can be used to calculate the distance between the object and the mirror. By rearranging the equation $m=-\frac{d_i}{d_0}$ , we can solve for $d_0$ .

Q: What is the relationship between the magnification of a real image and the focal length of the mirror?

A: The magnification of a real image is inversely proportional to the focal length of the mirror. As the focal length of the mirror increases, the magnification of the image decreases.

Q: Can the magnification of a real image be affected by the curvature of the mirror?

A: Yes, the magnification of a real image can be affected by the curvature of the mirror. Convex mirrors always produce reduced images, while concave mirrors can produce enlarged or reduced images depending on the distance between the object and the mirror.