Lens and mirror question, can't understand solution

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In summary, the problem involves a lens with a focal length of 0.8m and a mirror with a focal length of -0.500m. The object is placed 1.00m to the left of the lens and the light goes through the lens, bounces off the mirror, and goes through the lens again from the right. Using the formula 1/f=1/di+1/do, the image distance for the first lens is found to be 4.0m. The image distance for the mirror is -3.0m, indicating that the image is behind the mirror. The image distance for the second lens is found to be 1.6m, with a positive value due to the direction
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angelelizabeth
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Homework Statement


A lens of focal length 0.8m is 1.0 m to the left of a mirror of focal length -0.500m. An object is placed 1.00 m to the left of the lens. Light goes through the lens, bounces from the mirror, and goes through the lens again, this time from the right.


Homework Equations



1/f=1/di+1/do

The Attempt at a Solution



(THIS IS FROM THE OFFICIAL SOLUTION MANUAL, I AM CONFUSED ON PART OF THE ANSWER TOWARDS THE END)
1/di1=1/f1-1/do1
1/di1=1/0.8-1/1
di1=4.0 m

This image is 3 meters behind the mirror, so do2 for the mirror is -3.0 m.

1/di2=1/f2-1/do2
1/-0.5-1/-3=1/di2
di2= -0.6 m

This image is behind the mirror.

THIS IS WHERE I GET CONFUSED:
di3 (for the lens)=1+0.6m=1.6m

1/di2=1/f1-1/do3=1/0.8-1/1.6
di3=1.6m

In this instance, why is di3 postive 1.6 m instead of negative 1.6 meters? The "object" is to the right of the lens, so shouldn't di3 be negative?
 
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  • #2
If light is moving from left to right than left is positive and right is negative (that's the convention for an object), but if light is moving from right to left (and that's the case here) than right is positive and left is negative.
 

1. How do lenses and mirrors work?

Lenses and mirrors work by bending and redirecting light rays that pass through or reflect off of them. This bending of light allows for the formation of images, which can be used for various purposes such as magnification, projection, or correction of vision.

2. What is the difference between a lens and a mirror?

A lens is a piece of glass or other transparent material that bends light by refraction, while a mirror is a smooth, reflective surface that bends light by reflection. Lenses are typically used for magnifying or correcting vision, while mirrors are often used for reflecting light and creating images.

3. How does the focal length of a lens or mirror affect its function?

The focal length of a lens or mirror is the distance between the lens/mirror and the point where light rays converge or diverge. The shorter the focal length, the more powerful the lens/mirror is in bending light and creating images. A longer focal length results in a weaker bending of light.

4. What is the difference between a convex and concave lens or mirror?

A convex lens or mirror is thicker in the middle and thinner at the edges, while a concave lens or mirror is thinner in the middle and thicker at the edges. This difference in shape results in different light bending properties, with convex lenses/mirrors converging light and concave lenses/mirrors diverging light.

5. Can you explain the solution to a difficult lens and mirror problem?

Without specific context, it is difficult to provide a general solution to a lens and mirror problem. However, it is important to understand the properties of lenses and mirrors, such as focal length and curvature, and to use relevant equations, such as the thin lens equation or mirror equation, to solve the problem.

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