Lesson 6: Mirror Equation

Summary

This lesson explores the use of the mirror equation and magnification equation to determine the image characteristics formed by curved mirrors. Key concepts include understanding the relationships between object distance, image distance, focal length, and magnification. The lesson covers important sign conventions, provides step-by-step problem-solving examples using both equations, and illustrates the process through graphical methods. Students will learn to calculate image location, size, orientation, and type (real or virtual) for concave and convex mirrors, enhancing their understanding of image formation in optics.

Takeaways

• 😀 Ray diagrams help determine the location, size, orientation, and type of image formed by curved mirrors.
• 😀 The mirror equation relates object distance, image distance, and focal length: 1/f = 1/do + 1/di.
• 😀 The magnification equation helps determine the ratio of image height to object height or the ratio of image distance to object distance.
• 😀 Sign conventions for mirrors: positive focal length for concave mirrors, negative for convex mirrors; positive image distance indicates a real image, negative indicates a virtual image.
• 😀 The magnification is negative when the image is inverted, and positive when the image is upright.
• 😀 Doubling the focal length gives the radius of curvature (R = 2f).
• 😀 For concave mirrors, the focal length is positive, while for convex mirrors, it is negative.
• 😀 The image formed by a concave mirror is real and inverted when the image distance is positive.
• 😀 The image formed by a convex mirror is always virtual, upright, and smaller than the object.
• 😀 To calculate the image distance and size, use the mirror equation and magnification equation. The signs of the values play a crucial role in determining the image characteristics.

Q & A

What are ray diagrams used for in relation to curved mirrors?

Ray diagrams are used to determine the image's location, size, orientation, and type when objects are placed in front of curved mirrors.

How do the mirror and magnification equations relate to curved mirrors?

The mirror equation relates the object distance, image distance, and focal length, while the magnification equation connects the image distance, object distance, image height, and object height to determine the size and characteristics of the image formed by a curved mirror.

What does the mirror equation express mathematically?

The mirror equation expresses the quantitative relationship between the object distance (d_o), the image distance (d_i), and the focal length (f), as 1/f = 1/d_o + 1/d_i.

How is magnification related to the image and object sizes?

Magnification is the ratio of the image height to the object height, and it can also be expressed as the negative ratio of the image distance to the object distance.

What is the significance of the sign conventions for mirrors?

The sign conventions for mirrors help determine the type of image formed. For example, a positive focal length indicates a concave mirror, a positive image distance indicates a real image in front of the mirror, and a negative image distance indicates a virtual image behind the mirror.

How does the focal length relate to the radius of curvature?

The radius of curvature is twice the focal length. Mathematically, radius of curvature = 2f or f = radius of curvature / 2.

In the example with a concave mirror, what were the results of the image distance, magnification, and image height?

In the concave mirror example, the image distance was 60 cm, magnification was -2, and the image height was -10 cm, indicating the image is real, inverted, and enlarged.

What is the behavior of the image formed by a convex mirror?

In the convex mirror example, the image distance was -3 cm, magnification was 0.6, and the image height was 1 cm. This indicates the image is virtual, upright, smaller, and formed behind the mirror.

What does a negative magnification value indicate?

A negative magnification value indicates that the image is inverted relative to the object.

How can the mirror equation and magnification equation be applied to solve practical problems?

By using the mirror equation to find the image distance and then applying the magnification equation, we can calculate the size, location, and orientation of the image formed by a curved mirror based on known values such as object distance and focal length.