Simple Optics Problem (plane mirror and lens)

In summary: Some of the light reflected by the mirror will go through the lens. There are actually two images formed - one real and one virtual. The real image is located at 15 m from the lens and has a magnification of -1. The virtual image is located at 20 m from the origin and has a magnification of -1. This is because the light rays from the object first pass through the lens, creating a real image, and then are reflected by the mirror creating a virtual image. This is why the final location of the image is at 20 m and not 15 m as initially calculated.
  • #1
AKJ1
43
0

Homework Statement


A plane mirror is placed at the origin. A converging lens with a focal length of 5.00m is located at x=12.50m. A object is placed at x=22.5m

Find the final location of the image in terms of its X coordinate & magnification.

Homework Equations



1/q + 1/p = 1/f (lens)

1/q = -1/p (plane mirror; focal length is infinite)

q = image distance
p= object distance

The Attempt at a Solution


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So I first find the distance from the lens to the object (10m), then following from the equation

1/q + 1/p = 1/f

1/q +1/10 = 1/5

q = 10m

Now we consider the mirror. The image from the lens will serve as the object for the mirror.

1/q = -1/p

1/q = -1/10

q = -10m ?

However the answer says 20m. I just started studying geometric optics (I have yet to have a formal lecture on it), so I am likely missing something fundamental here. Is there another image somehow formed?

Thanks
 
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  • #2
AKJ1 said:
So I first find the distance from the lens to the object (10m), then following from the equation

1/q + 1/p = 1/f

1/q +1/10 = 1/5

q = 10m

Looks good so far.

Now we consider the mirror. The image from the lens will serve as the object for the mirror.

1/q = -1/p

1/q = -1/10

Yes, the image of the lens serves as the object for the mirror. But, 10 m is not what you should use for the object distance for the mirror. A diagram where you show the image of the lens should help.
 
  • #3
The light reflected from the mirror will pass through the lens - making another image.
Try sketching a ray diagram.
 
  • #4
TSny said:
Looks good so far.
Yes, the image of the lens serves as the object for the mirror. But, 10 m is not what you should use for the object distance for the mirror. A diagram where you show the image of the lens should help.

Okay so I sketched a diagram. The 10m I got is the distance from the lens, so that distance from the mirror is actually 2.5m

1/q = -1/p

1/q = -1/2.5

q = -2.5 m

The image is virtual and behind the mirror (Correct?)

So now the distance from the lens is (12.5-(-2.5)) = 15 m

1/p + 1/q = 1/f

1/15 + 1/q = 1/5 (Is the focal length still positive because we have a convex lens?)

q = 7.5 m, but the distance from the origin is 12.5 + 7.5 = 20m

Okay assuming I did it correctly, how do I know how many images will be formed in any system? Will I just need to take it step by step and realize that mirrors will reflect light back to the lens?

Thank you!
 
  • #5
Simon Bridge said:
The light reflected from the mirror will pass through the lens - making another image.
Try sketching a ray diagram.

Will a mirror always reflect light back in the direction of which it originated? Or does this depend on the type of mirror?
 
  • #6
Will a mirror always reflect light back in the direction of which it originated? Or does this depend on the type of mirror?
The mirror will always reflect light back into the space that the light came from - that is what reflect means. The alternative would be if the mirror somehow reflected light through itself ... there are objects that do that, they are called windows.

Some of the light reflected by the mirror will go through the lens.
 

Related to Simple Optics Problem (plane mirror and lens)

1. What is a plane mirror and how does it work?

A plane mirror is a flat reflective surface that reflects light in a predictable manner. It works by reflecting light rays at an angle equal to the angle at which they strike the mirror's surface, creating a virtual image that appears to be behind the mirror.

2. How do you calculate the image distance in a plane mirror?

The image distance in a plane mirror is equal to the object distance (the distance from the object to the mirror). This is because the virtual image created by a plane mirror is the same distance behind the mirror as the object is in front of it.

3. What is the difference between a real and virtual image in a plane mirror?

A real image is one that can be projected onto a screen, while a virtual image cannot. In a plane mirror, the image formed is always virtual, meaning it cannot be projected onto a screen.

4. What is the focal length of a lens and how is it calculated?

The focal length of a lens is the distance between the lens and the point where parallel light rays converge to a single point. It can be calculated using the lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

5. How does a lens refract light and form an image?

A lens refracts light by bending the light rays as they pass through the lens, creating an image on the opposite side of the lens. The shape of the lens determines the amount and direction of this bending, resulting in either a converging or diverging lens. The image formed by a lens can be real or virtual, depending on the position of the object relative to the lens.

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