Optics: finding the width of an image produced through a lens

[randomperson]

Homework Statement

This is more of a general conceptual question.

When finding the image produced through a convex or concave lens, I know that you can use the equation magnification = (height of image/height of object) to find the magnification of the image produced. But does this proportion extend to the width of the object and image as well?

For example, if I had an object that was 5 inches tall and 6 inches wide, and the magnification was -2, what would be the dimensions of the image produced?

Homework Equations

mag = hi/ho = -di/do

The Attempt at a Solution

I know that the height of the image would be is -10 inches. Would the width of the image simply be -12 inches?

Also if that is how you find it, would width be given as a positive value or negative value? The height would be negative by convention because the image is flipped, but is width is negative as well? (I’m thinking yes, because when an image is inverted, you see an upside down and backwards image, so the left side of the object shows up on the right side of the image, etc.)

 

[anathema]

Thank you for your question. The equation for magnification, as you have correctly stated, is m = hi/ho = -di/do. This equation can be applied to both the height and width of the object and image. In your example, if the object is 5 inches tall and 6 inches wide, and the magnification is -2, then the resulting image will be -10 inches tall and -12 inches wide.

The negative values for height and width indicate that the image is inverted, as you mentioned. This is because the light rays are refracted at different angles as they pass through the lens, causing the image to be flipped. Therefore, the width will also be negative, as the left side of the object will appear on the right side of the image.

I hope this answers your question. If you have any further inquiries, please don't hesitate to ask. As scientists, we are always happy to help clarify any conceptual or mathematical questions. Keep up the great work!