Concept explainers
A telephoto lens consists of a positive lens of focal length +3.5 cm placed 2.0 cm in front of a negative lens of focal length –1.8 cm. (a) Locate the image of a very distant object. (b) Determine the focal length of the single lens that would form as large an image of a distant object as is formed by this lens combination.
(a)
The distance of the image of an object, which is very far away from the telephoto lens, if it has a positive focal length of
Answer to Problem 33SP
Solution:
A real image at a distance of
Explanation of Solution
Given data:
The focal length of the negative lens is
The focal length of the positive lens is
The positive lens is placed
Formula used:
The expression for the thin lens formula is written as
Here,
Sign convention:
Explanation:
Draw the diagram according to the problem.
Here,
Understand that for the given diagram, the image of the object at very distant formed at the focus of the positive lens, which works as an object for the negative lens. So, the distance of the object from the negative lens will be the difference between its focal length and the distance between both the lenses.
The expression for the distance of the object from a negative lens is
Substitute
Also, the object will be at right side for negative lens. So, its distance will be negative according to the sign convention. Therefore,
Write the expression for the lens formula for a thin lens:
Substitute
The positive sign of the distance of the image shows that a real image is formed
Conclusion:
Hence, the image formed of a very distant object from the telephoto is real and
(b)
The focal length of a single lens that will form as large image of distant object as formed by the combination of a positive lens of focal length
Answer to Problem 33SP
Solution:
Explanation of Solution
Given data:
The focal length of the positive lens is
The focal length of the negative lens is
The positive lens is placed
Formula used:
The expression for the resultant focal length of a combination of lenses is written as
Explanation:
Recall the expression for the resultant focal length of a combination of lenses:
Substitute
Conclusion:
The focal length of the single lens will be
Want to see more full solutions like this?
Chapter 39 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
- A converging lens made of crown glass has a focal length of 15.0 cm when used in air. If the lens is immersed in water, what is its focal length? (a) negative (b) less than 15.0 cm (c) equal to 15.0 cm (d) greater than 15.0 cm (e) none of those answersarrow_forwardA lamp of height S cm is placed 40 cm in front of a converging lens of focal length 20 cm. There is a plane mirror 15 cm behind the lens. Where would you find the image when you look in the mirror?arrow_forwardWhat is the magnification of a magnifying lens with a focal length of 10 cm if it is held 3.0 cm from the eye and the object is 12 cm from the eye?arrow_forward
- You view an object by holding a 2.5 cm-focal length magnifying glass 10 cm away from it. How far from your eye should you hold the magnifying glass to obtain a magnification of 10 ?arrow_forwardAn object of height 3 cm is placed at a distance of 25 cm in front of a converging lens of focal length 20 cm, to be referred to as the first lens. Behind the lens there is another converging lens of focal length 20 cm placed 10 cm from the first lens. There is a concave mirror of focal length 15 cm placed 50 cm from the second lens. Find the location, orientation, and size of the final image.arrow_forwardThe left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is 1.44. (a) Calculate the focal length of the lens for light incident from the left. (b) What If? After the lens is turned around to interchange the radii of curvature of the two faces, calculate the focal length of the lens for light incident from the left.arrow_forward
- A converging lens has a focal length of 10.0 cm. Locate the object if a real image is located at a distance from the lens of (a) 20.0 cm and (b) 50.0 cm. What If? Redo the calculations if the images are virtual and located at a distance from the lens of (c) 20.0 cm and (d) 50.0 cm.arrow_forwardWhat will be the formula for the angular magnification of a convex lens of focal length f if the eye is very close to the lens and the near point is located a distance D from the eye?arrow_forwardIn Figure P26.38, a thin converging lens of focal length 14.0 cm forms an image of the square abcd, which is hc = hb = 10.0 cm high and lies between distances of pd = 20.0 cm and pa = 30.0 cm from the lens. Let a, b, c, and d represent the respective corners of the image. Let qa represent the image distance for points a and b, qd represent the image distance for points c and d, hb represent the distance from point b to the axis, and hc represent the height of c. (a) Find qa, qd, hb, and hc. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a and d, for which the object distance is p. Let h represent the distance from the axis to the point at the edge of the image between b and c at image distance q. Demonstrate that h=10.0q(114.01q) where h and q are in centimeters. (d) Explain why the geometric area of the image is given by qaqdhdq (e) Carry out the integration to find the area of the image. Figure P26.38arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning