The distance between the image and the surface 2 and the magnification of the final image.
Answer to Problem 39PQ
The distance of the screen from the surface 2 is
Explanation of Solution
Write the expression for the refraction at a spherical surface.
Here,
Rearrange the equation (I) for
Write the expression for the magnification for a refractive surface.
Here,
Write the expression for the total magnification for a thick lens.
Here,
Conclusion:
Substitute
The positive sign indicates that the image is formed on the right side of surface 1.
Substitute
The image formed by surface 1 acts as the object for the surface 2. Thus, the object distance for surface 2 is,
Substitute
The positive sign indicates that the image is formed behind the surface 2.
Substitute
Substitute
Therefore, the distance of the screen from the surface 2 is
Want to see more full solutions like this?
Chapter 38 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- People who do very detailed work close up, such as jewelers, often can see objects clearly at much closer distance than the normal 25 cm. (a) What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.00 cm? (b) What is the image size of a 1.00-mm object, such as lettering inside a ring, held at this distance? (c) What would the size of the image be if the object were held at the normal 25.0 cm distance?arrow_forwardA doctor examines a mole with a 15.0-cm focal length magnifying glass held 13.5 cm from the mole. (a) Where is the image? (b) What is its magnification? (c) How big is the image of a 5.00 mm diameter mole?arrow_forwardIn Figure P35.30, a thin converging lens of focal length 14.0 cm forms an image of the square abed, which is he = 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 P35.30arrow_forward
- An object (height = 7.7 cm) and its image are on opposite sides of a converging lens. The object is located 14.0 cm from the lens. The image is located 5.6 cm from the lens. Determine the image height (in cm). Enter the numerical part of your answer to two significant figures. Hint: Remember that the sign of the image height is significant.arrow_forwardAn object is placed 96.5 cm from a glass lens (n = 1.51) with one concave surface of radius 22 cm and one convex surface of radius 19.3 cm. Determine the final image distance from the center of lens. Follow the sign conventions. Express your answer to two significant figures and include the appropriate units. di=? What is the magnification? Follow the sign conventions. Express your answer using two significant figures. m=?arrow_forward1. You have a thin lens of focal length 50 mm. a. The object is 100 mm to the left of the lens. Where is the image located (that is, what is the image distance q, including sign - express in millimeters)? Is the image real or virtual? What is the magnification? b. The object is 1 meter to the left of the lens. Where is the image located (that is, what is the image distance q, including sign - express in millimeters)? Is the image real or virtual? What is the magnification? c. The object is 20 mm to the left of the lens. Where is the image located (that is, what is the image distance q, including sign - express in millimeters)? Is the image real or virtual? What is the magnification?arrow_forward
- A converging lens with a focal length of 40 cm and a diverging lens with a focal length of −36 cm are 156 cm apart. A 3.3-cm-tall object is 60 cm in front of the converging lens. a. Calculate the image height. hi=arrow_forwardA convex lens is set up on a table. On one side is an illuminated object of size 8 cm that is 41 cm from the lens. The focal length of the lens is 9 cm. 1. Where will the image be located, i.e. q (in cm)? 2. What will be the magnification? 3. Will the image be real or inverted? 4. Will the image be upright or inverted? 5. What will be the size of the image. In canvas, write only the magnitude of the size in cm. For a convex lens, 'p' and 'f' are positive.arrow_forwardA small air bubble is 4.2 cm below the top surface of a glass (n = 1.52) sphere with a 15 cm radius. To a person viewing this from above, where is the image? Give the distance of the image from the surface and say whether the image is inside the sphere or outside it.arrow_forward
- A convex lens produces a real, inverted image of an object that is magnified 2.5 times when the object is 20 cm from the lens. a) What is the image distance of the lens? di = b) What is the focal length of the lens? f =arrow_forwardq37 An object (height = 8.2 cm) and its image are on opposite sides of a converging lens. The object is located 19.0 cm from the lens. The image is located 5.5 cm from the lens. Determine the magnification. Enter the numerical part of your answer to two significant figures. Hint: Remember that the sign of the magnification is significant.arrow_forwardAn object is 12.0 cm from a converging lens (focal length = 15.0 cm). Determine the image magnification. Enter the numerical part of your answer to two significant figures. Hint: Remember that the sign of the magnification is significant.arrow_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