Hi guys, I'm a little stuck on this question I'm doing at the moment. If anyone has spare time, I'd be extremely grateful!
A lens with 50-cm focal length produces a real image the same size as the object.
a)How far from the lens is the object?
b)How far from the lens is the image?
What I've done:
Ok...I'm looking through my textbook and the only equation that seems to fit is:
1/s+1/s'=1/f
where s: image distance in front of mirror
s': image distance behind the mirroe
f:focal length
(If my equation is wrong, just shout out! I don't care!)
But the problem is I have too many unknowns...I'm so stumped.
Anyway, just wanted to thank the incredible person who helps me in this question in advance! You da MVP!
Hi there! I'll be happy to help you with this question step-by-step.
The lens formula you mentioned, 1/s + 1/s' = 1/f, is indeed the correct formula for thin lenses. Let's use it to solve the problem.
a) To find the distance of the object from the lens, we need to find the image distance (s') and the focal length (f). Since the real image is the same size as the object, the magnification (m) is 1. The magnification formula is m = -s'/s. Therefore, we can write 1 = -s'/s.
We also know that the focal length (f) is 50 cm. So we can substitute these values into the lens formula: 1/s + 1/s' = 1/f.
Substituting 1 for m and -s' for s in the magnification formula, we get: 1 = -s'/s. Rearranging this equation, we get s = -s'.
Substituting these values into the lens formula, we have 1/s + 1/-s = 1/50. Simplifying this equation further, we get: 1/s - 1/s = 1/50.
Combining the terms, we have 2/s = 1/50. Solving for s, we get s = 50/2. Therefore, the distance of the object from the lens is 25 cm.
b) Now, let's find the distance of the image from the lens. We already found that s = 25 cm. Using the lens formula, we can find s':
1/s + 1/s' = 1/f
Substituting the values we know, we have: 1/25 + 1/s' = 1/50.
Rearranging this equation, we have: 1/s' = 1/50 - 1/25.
Combining the terms, we get: 1/s' = 2/50 - 1/50.
Simplifying further, we have: 1/s' = 1/50. Solving for s', we find that s' = 50.
Therefore, the distance of the image from the lens is 50 cm.
So, to summarize:
a) The object is 25 cm away from the lens.
b) The image is 50 cm away from the lens.
I hope this helps! Let me know if you have any further questions.
Hi there! I can help you with this question. Don't worry, we'll figure it out together!
For a lens with a focal length of 50 cm, we can use the lens formula to find the answers to parts (a) and (b).
The lens formula you mentioned is correct: 1/s + 1/s' = 1/f.
Here, s represents the object distance, s' represents the image distance, and f is the focal length.
In this case, since the lens produces a real image the same size as the object, we know that the magnification (m) is equal to 1.
The magnification (m) is given by the formula: m = -s'/s, where the negative sign indicates that the image is inverted.
To solve for the unknowns, we need to use both the lens formula and the magnification formula.
Let's start with part (a), finding the distance of the object from the lens.
We know that the magnification (m) is 1, so substituting the values into the magnification formula, we get:
1 = -s'/s
Since the magnification is 1, this means that the image distance (s') is equal to the object distance (s), but with opposite signs. So:
s' = -s
Now, we can substitute this into the lens formula:
1/s + 1/(-s) = 1/f
Simplifying this equation, we get:
1/s - 1/s = 1/f
0 = 1/f
Since f is not equal to zero, this equation does not have a solution. This means that it is not possible for the object to be at any finite distance from the lens in order to produce a real image the same size as the object.
Therefore, part (a) does not have a valid solution.
For part (b), finding the distance of the image from the lens:
Since part (a) does not have a valid solution, there is no image formed by the lens. Therefore, part (b) does not have a valid solution either.
I hope this explanation helps you understand the problem! If you have any more questions, feel free to ask.