Finding the distance in an optics system

In summary, the conversation discusses the correct approach to solving for mirrors and lenses, using the equations ##\dfrac {1}{p}+\dfrac {1}{q}=\dfrac {1}{f}## and ##\dfrac {1}{x+13.333}+\dfrac {1}{x}=\dfrac {1}{-10}##. The equation for the lens is quadratic, resulting in two solutions for the distance between the mirror and lens, with one being positive and greater than 20 cm. The image will always be virtual if the object and image are on the same side of the lens. However, with a mirror, the image will be virtual if it is formed behind the mirror.
  • #1
jisbon
476
30
Homework Statement
An object is located 20cm to the left of a concave mirror (with curvature 10cm). Light leaves object is the first incident on the mirror and passes through the lens of 10cm in focal length located left of the object. A final image formed by the system is located a the same location as the original object.

i) Find distance between lens and mirror
ii) Comment on orientation and magnification of the final image
Relevant Equations
##\dfrac {1}{p}+\dfrac {1}{q}=\dfrac {1}{f}##
Hi all,
Pretty new to optics here, so would like to get my basics right.
Below is my working, was wondering if my concepts are correct here.

First I will separate mirror and lens and solve them 1 by 1, so solving for mirror first,

##\dfrac {1}{p_{1}}+\dfrac {1}{q_{1}}=\dfrac {1}{f_{1}} ## where ##p_{1}## is the object distance to mirror and ##q_{1}## is the image distance to mirror.
Putting ##p_{1}## as 20cm and ##{f_{1}}## as 5cm (since f=R/2) , I get ##q_{1}## to be 20/3 cm
From what I understand, since ##q_{1}## is positive, this means it is infront of the mirror, so it should be something like:
1578569667464.png

this?
Assuming this is correct,

Now moving on to the lens,
##\dfrac {1}{p_{2}}+\dfrac {1}{q_{2}}=\dfrac {1}{f_{2}} ##
let x be the distance between between object and lens,
so from the above equation,
Taking ##p_{2}## = distance between object and lens
and
##q_{2}## = distance between image and lens
##\dfrac {1}{p_{2}}+\dfrac {1}{q_{2}}=\dfrac {1}{f_{2}} ##
where the new object is the image projected by the mirror,
##\dfrac {1}{x+13.333}+\dfrac {1}{x}=\dfrac {1}{-10} ##
and from here I can find x where (i) will be x +20cm

Is this correct? Thanks
 
Physics news on Phys.org
  • #2
That all looks right to me. On to part (ii)
 
  • #3
jisbon said:
##\dfrac {1}{x+13.333}+\dfrac {1}{x}=\dfrac {1}{-10} ##
and from here I can find x where (i) will be x +20cm
Is this correct? Thanks
The equation you have is correct, however it is quadratic in ##x## which means two solutions. Which one will you use and how?

On Edit: The equation is almost correct. You have to be careful about what ##x## is and how you use it in the equation. I would strongly recommend that you define ##x## as what you are looking for, namely the distance between the mirror and the lens. Then one of the solutions should come out positive and greater than 20 cm. The second solution should be something obvious in retrospect.
 
Last edited:
  • #4
kuruman said:
The equation you have is correct, however it is quadratic in ##x## which means two solutions. Which one will you use and how?

On Edit: The equation is almost correct. You have to be careful about what ##x## is and how you use it in the equation. I would strongly recommend that you define ##x## as what you are looking for, namely the distance between the mirror and the lens. Then one of the solutions should come out positive and greater than 20 cm. The second solution should be something obvious in retrospect.

There are 2 solutions to x,
1578634128978.png

In this case taking x to be -28..68517 will make more sense, but I don't actually understand why in this case.
Following your edit:

##\dfrac {1}{x-\dfrac {20}{3}}+\dfrac {1}{x-20}=\dfrac {1}{-10} ## where x is the distance between mirror and lens
1st term: distance between obj and lens
2nd term: distance between image and lens
3rd term: focal length
I got:
1578634471348.png


which seems to be wrong since x must be more than 20cm?
 
  • #5
jisbon said:
There are 2 solutions to x, View attachment 255394
In this case taking x to be -28..68517 will make more sense, but I don't actually understand why in this case.
Following your edit:

##\dfrac {1}{x-\dfrac {20}{3}}+\dfrac {1}{x-20}=\dfrac {1}{-10} ## where x is the distance between mirror and lens
1st term: distance between obj and lens
2nd term: distance between image and lens
3rd term: focal length
I got: View attachment 255396

which seems to be wrong since x must be more than 20cm?
x-20 is the Physical distance between image and lens, but you need to use it with negative sign if the image is virtual.
 
  • #6
Oops! I didn’t catch it when I looked at it the first time. Sorry about that. In your final equation you write

##\frac {1} {x + 13.333} + \frac 1 x = \frac 1 {-10}##

but both the object and the image are on the same side of the lens. That means the image is virtual and the position should be negative
 
  • #7
Cutter Ketch said:
Oops! I didn’t catch it when I looked at it the first time. Sorry about that. In your final equation you write

##\frac {1} {x + 13.333} + \frac 1 x = \frac 1 {-10}##

but both the object and the image are on the same side of the lens. That means the image is virtual and the position should be negative
Will the image always be virtual if the object and the image are on the same side of the lens (regardless of lens?/mirror even?)
 
  • #8
jisbon said:
Will the image always be virtual if the object and the image are on the same side of the lens (regardless of lens?/mirror even?)
An image is virtual if it is formed where light has no business being relative to the object: behind a mirror and in front of a lens.
 
  • Like
Likes jisbon and hutchphd
  • #9
jisbon said:
Will the image always be virtual if the object and the image are on the same side of the lens (regardless of lens?/mirror even?)
Lens, yes. Mirror, vice versa.
 
  • Like
Likes jisbon
  • #10
Ah yes okay, thanks for all your help :)

kuruman said:
An image is virtual if it is formed where light has no business being relative to the object: behind a mirror and in front of a lens.
Cutter Ketch said:
Lens, yes. Mirror, vice versa.
 

What is the formula for finding the distance in an optics system?

The formula for finding the distance in an optics system is d = f * (1/u - 1/v), where d is the distance between the object and the image, f is the focal length of the lens, u is the distance between the object and the lens, and v is the distance between the image and the lens.

What is the difference between object distance and image distance?

Object distance refers to the distance between the object and the lens in an optics system, while image distance refers to the distance between the image and the lens. The two distances are related by the formula d = f * (1/u - 1/v).

How does the focal length of a lens affect the distance in an optics system?

The focal length of a lens determines the strength of the lens and therefore affects the distance in an optics system. A lens with a shorter focal length will produce a larger image at a shorter distance, while a lens with a longer focal length will produce a smaller image at a longer distance.

Why is it important to find the distance in an optics system?

Finding the distance in an optics system is important because it allows for the accurate and precise positioning of objects and lenses to create clear and focused images. It is also necessary for determining the magnification of an image and understanding the properties of a lens.

What factors can affect the accuracy of finding the distance in an optics system?

Some factors that can affect the accuracy of finding the distance in an optics system include the precision of measurements, the quality of the lens, and the presence of any aberrations or distortions. It is important to use proper techniques and equipment to minimize these potential sources of error.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
746
  • Introductory Physics Homework Help
Replies
17
Views
411
  • Introductory Physics Homework Help
Replies
21
Views
187
  • Introductory Physics Homework Help
Replies
7
Views
914
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
964
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
814
  • Introductory Physics Homework Help
Replies
8
Views
956
  • Introductory Physics Homework Help
Replies
21
Views
1K
Back
Top