Reference no: EM131635554
This is a two part question.
Part 1. To look closely at a small object, such as an insect or a crystal, you bring it close to your eye, making the subtended angle and the retinal image as large as possible. But your eye cannot focus sharply on objects that are closer than the near point, so the angular size of an object is greatest when it is placed at the near point (25 cm away from a "normal" eye). To enlarge the object even more, one uses a magnifying glass, which is a converging lens that produces a virtual image that is larger and further away from the eye than the object is. The usefulness of the magnifying glass is given by the angular
magnification
m ang= θ′/θ
which is the ratio of the angular size θ′ of the image seen through a magnifier when the object is placed at the magnifier's focal point to the largest angular size θ of the object (when you view it from the near point)1. Find the angular magnification of a magnifying glass made of a converging lens with a focal length of 5 cm, assuming that the person who uses it has perfect vision.
Part 2. In an astronomical telescope the image formed by an objective is viewed through an eyepiece. To have the final image formed at infinity (for most comfortable viewing by a normal eye), the distance between objective and eyepiece, which is the length of the telescope, is made equal to the sum of the focal lengths of objective f1 and eyepiece f2. Find the angular magnification (see the definition above) of a telescope with f1 = 100 cm and f2 = 10 cm, which is defined (similar to above) as the ratio of the angle subtended at the eye by the final image to the angle subtended at the (unaided) eye by the object: mang = θ′/θ. Find the height of the image formed by the objective of a 20-story building 60 m tall, 3 km away. What is the angular size of the final image as viewed by an eye very close to the eyepiece?
Foot Note 1: One should not confuse the angular magnification mang with the (lateral) magnification m = -s′/s. Angular magnification is the ratio of the angular size of an image to the angular size of the corresponding object; lateral magnification refers to the ratio of the height of an image to the height of the corresponding object. For the situation discussed in the problem, the angular magnification is typically from 2 to 10. The lateral magnification, however, is infinite in this case, because the virtual image produced by the magnifying glass is at infinity (s′ = ∞), but that does not mean that objects looks infinitely large through the magnifier!
An unbiased watchdog over political institutions
: to what extent do the media act as an unbiased watchdog over political institutions?
|
Evaluate the likelihood that mental health institutions
: Evaluate the likelihood that mental health institutions, overall, may maintain their financial status through sustained growth.
|
What is your take on a iot and cloud ecosystem
: How can we reliably account for the depreciation in intellectual assets in a firm? What is your take on a "IoT and cloud" ecosystem?
|
What is the magnitude of c
: What is the magnitude of C, where C = A + B? Remember that 370 is (close enough) the smallest angle of a 3,4,5 right-angle triangle.
|
Usefulness of the magnifying glass
: To look closely at a small object, such as an insect or a crystal, you bring it close to your eye, making the subtended angle and the retinal image as large.
|
A powerful component of the us government
: What makes the Bureaucracy such a powerful component of the U.S. government? what has allowed it to become so powerful?
|
What is the magnitude of vector a+b
: Vector A, with length 8 units, points along the x axis. A second vector B, with magnitude 3 units, makes an angle of 60° with the x axis.
|
Explore the technology systems
: Explore the technology systems offered by Nanthealth, a provider of "telehealth" and health management services
|
How well does your organization manage customer expectations
: How well does your organization manage customer expectations? How is this substantiated or proven to an unbiased, external third-party? Give examples.
|