QQuestionPhysics
QuestionPhysics
At what two points between object and screen may a converging lens with a 3.80 cm focal length be placed to obtain an image on the screen?
Express your answers in centimeters separated by a comma. Count the distances from the object.
## Part B
What is the magnification of the image for each position of the lens?
Express your answer as two numbers, separated by a comma.
Submit Request Answer
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Set up the thin lens equation
We are given the focal length $$f = 3.80 \, \text{cm}$$.
We need to find the two positions where the lens can be placed such that an image is formed on the screen. This means that the image distance will always be positive.
Step 2:: Solve for the image distance (d_{i}) in terms of the object distance (d_{o})
d_{i} = \left(\frac{1}{f} - \frac{1}{d_{o}}\right)^{-1}
Step 3:: Find the first position of the lens
d_{i1} = \left(\frac{1}{3.80 \, \text{cm}} - \frac{1}{d_{o1}}\right)^{-1}
We want to find the image distance d_{i^1} using the formula from Step 2. To form a real, inverted image on the screen, the image distance must be positive. We also know that the object is located between the focal point and the lens, so the object distance is between the focal length and zero:
Step 4:: Find the second position of the lens
d_{i2} = \left(\frac{1}{3.80 \, \text{cm}} - \frac{1}{d_{o2}}\right)^{-1}
We want to find the image distance d_{i^2} using the formula from Step 2. To form a real, inverted image on the screen, the image distance must be positive. This time, the object is located at a distance greater than twice the focal length from the first image position. This ensures that the lens forms a virtual, upright image of the object at the second position:
Step 5:: Calculate the magnifications
m_{2} = -\frac{d_{i2}}{d_{o2}}
The magnification of an image formed by a lens is given by the formula: Calculate the magnifications for both positions of the lens:
Final Answer
The two positions of the lens are: d_{o^1} = \boxed{????} \, \text{cm} d_{o^2} = \boxed{????} \, \text{cm} The magnifications for these positions are: m_{1} = \boxed{????} m_{2} = \boxed{????} Since the problem does not provide specific values for the object distance, we cannot provide exact numerical answers. Instead, we have shown the formulas and steps to find the two positions of the lens and their corresponding magnifications. To find the actual values, substitute the given focal length and the appropriate object distances into the formulas from Steps 3, 4, and 5.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students