Physics 59 Optical Instruments (1 of 20) Magnifying Glass

Michel van Biezen
7 May 201309:47
EducationalLearning
32 Likes 10 Comments

TLDRThis lecture delves into the workings of a magnifying glass, the simplest optical instrument. It explains how placing an object at the focal length with relaxed vision creates a virtual image with increased angular size, thus magnifying the object. The script clarifies the concept of magnification as the ratio of the new to the original angular size. It also explores the mathematical relationship between the object's distance, the lens's focal length, and the resulting magnification, both with relaxed and strained vision, providing formulas and examples to calculate magnification in different scenarios.

Takeaways
  • ๐Ÿ” The simplest optical instrument is the magnifying glass, which works by altering the angular size of an object to make it appear larger.
  • ๐Ÿ‘€ Angular size (ฮธ) is the ratio of the object's height (H) to its distance from the observer, determining how large the object appears.
  • ๐ŸŒŸ When using a magnifying glass, the object is placed at the focal length (F) from the lens, creating a virtual image that appears larger due to the increased angular size.
  • ๐Ÿ“ The magnification of a magnifying glass is the ratio of the new angular size (ฮธ') to the original angular size (ฮธ).
  • ๐Ÿ“š The tangent of an angle in a right triangle can be used to calculate the magnification, where the tangent of ฮธ is H/distance and ฮธ' is H/F.
  • โ‰ˆ For small angles, the tangent of the angle is approximately equal to the angle itself, simplifying the calculation of magnification.
  • โš–๏ธ Magnification is calculated as 25/F when the object is placed at the focal length, where 25 cm is the distance from the observer to the image.
  • ๐Ÿ”ข If the focal length of the lens is 10 cm, the magnification is 2.5, indicating the object appears 2.5 times larger than its actual size.
  • ๐Ÿ‘๏ธ 'Relaxed vision' means placing the object at or near the focal point, resulting in an image formed far away that can be viewed comfortably.
  • ๐Ÿ‘“ 'Strain vision' is used when the object is placed closer to the lens than the focal length, resulting in a larger image formed at a closer distance.
  • ๐Ÿ“ To find the exact object distance for a specific image distance, solve the lens equation for s, which relates object distance (s), image distance (s'), and focal length (F).
  • ๐Ÿ“š The general formula for magnification when the image is formed at a distance of 25 cm (with strain vision) is 25/F + 1, providing a larger magnification than with relaxed vision.
Q & A

  • What is the simplest optical instrument discussed in the script?

    -The simplest optical instrument discussed in the script is the magnifying glass.

  • What is meant by the angular size of an object?

    -The angular size of an object is the angle it subtends at the eye, which is the ratio of the object's height to the distance from the object to the observer.

  • How does placing an object closer to the observer with a magnifying glass change its angular size?

    -When an object is placed closer to the observer with a magnifying glass, the angular size appears larger because the ratio of the object's height to the distance is increased.

  • What is the relationship between the magnification of a magnifying glass and the focal length of the lens?

    -The magnification of a magnifying glass is equal to 25 divided by the focal length of the lens when the object is placed at the focal point with relaxed vision.

  • What is relaxed vision in the context of using a magnifying glass?

    -Relaxed vision means looking at the object placed at or just very near the focal point of the lens, allowing the observer to see a virtual image behind the object without straining the eyes.

  • How does the position of the object relative to the lens affect the magnification?

    -If the object is placed closer to the lens than the focal length, the magnification increases because the image is formed closer to the observer, allowing for strain vision and a larger apparent size.

  • What is the formula for calculating the magnification of a magnifying glass with relaxed vision?

    -The formula for calculating the magnification with relaxed vision is magnification = 25 / F, where F is the focal length of the lens.

  • What is meant by strain vision when using a magnifying glass?

    -Strain vision refers to looking at an image that is formed closer to the observer than the normal viewing distance, which can be achieved by moving the object closer to the lens than the focal point.

  • How can you calculate the new magnification when using strain vision with a magnifying glass?

    -The new magnification when using strain vision can be calculated using the formula magnification = 25 / F + 1, where F is the focal length of the lens.

  • What is the significance of the tangent of theta and theta prime in the script?

    -The tangent of theta and theta prime are used to approximate the small angles in the geometric representation of the magnifying glass setup, allowing for the simplification of the magnification calculation.

  • How does the script explain the relationship between the object distance and the image distance in a magnifying glass setup?

    -The script explains that when the object is placed very close to the focal point, the image distance becomes very large, allowing for relaxed vision. Conversely, moving the object closer to the lens than the focal length results in a smaller image distance, requiring strain vision.

Outlines
00:00
๐Ÿ” Understanding Magnifying Glass Basics

This paragraph introduces the concept of using a magnifying glass to enlarge the appearance of an object. It explains the principle of angular size (theta) as the ratio of object height to the distance from the observer. The magnifying glass is placed at the focal length from the observer, creating a virtual image that increases the angular size (theta prime), thus magnifying the object. The magnification is determined by the ratio of theta prime to theta. The tangent function is used to relate the object's height to the distance, and for small angles, the tangent of theta is approximated as theta itself. The formula for magnification is derived as 25 divided by the focal length of the lens, exemplified with a lens having a 10-centimeter focal length, resulting in a 2.5x magnification.

05:05
๐Ÿ‘€ Adjusting Magnification with Object Placement

The second paragraph delves into how the placement of the object affects the magnification power of a magnifying glass. It discusses two scenarios: looking through the lens with relaxed vision, where the object is placed at or near the focal point, and looking with strain vision, where the object is moved closer to the lens to form a larger image at a set distance (25 centimeters in this case). The mathematical relationship between object distance, image distance, and focal length is explored to calculate the new object distance required for the desired magnification. The general formula for magnification is provided, which includes an additional 'plus one' factor when using strain vision. An example calculation is given for a lens with a 10-centimeter focal length, showing that moving the object to 7.14 centimeters from the lens results in a 3.54x magnification.

Mindmap
Keywords
๐Ÿ’กOptical instruments
Optical instruments refer to devices that use the principles of optics to form images or to manipulate light for various purposes. In the context of the video, the focus is on magnifying glasses, which are a type of optical instrument used to enlarge the appearance of objects. The script discusses how magnifying glasses work and their magnification properties.
๐Ÿ’กMagnifying glass
A magnifying glass is a convex lens that is used to magnify the appearance of small objects. It is the simplest optical instrument discussed in the video. The script explains how a magnifying glass works by placing an object at a certain distance from the lens to create a larger virtual image.
๐Ÿ’กAngular size
Angular size is the measure of the angle that an object subtends at the eye of an observer. It is a key concept in the video, as it is used to describe the perceived size of an object without and with the use of a magnifying glass. The script explains that the angular size is the ratio of the object's height to its distance from the observer.
๐Ÿ’กFocal length
The focal length of a lens is the distance from the lens to the point where parallel light rays converge after passing through the lens. In the script, the focal length is crucial in determining the magnification power of a magnifying glass. The video uses the focal length to calculate the magnification when an object is placed at this distance.
๐Ÿ’กVirtual image
A virtual image is an image that appears to be located where light rays do not actually converge, but rather seem to diverge from. The script mentions that when an object is placed at the focal length of a magnifying glass, a virtual image is formed behind the object, which contributes to the magnification effect.
๐Ÿ’กMagnification
Magnification is the process of making an object appear larger than its actual size. The video script explains how magnification is achieved with a magnifying glass and how it is calculated by comparing the angular size of the object with and without the lens.
๐Ÿ’กTangent
In the context of the video, the tangent of an angle is the ratio of the opposite side to the adjacent side in a right-angled triangle. The script uses the tangent function to relate the height of the object and the image to their respective distances from the observer, which helps in calculating the magnification.
๐Ÿ’กRelaxed vision
Relaxed vision refers to the condition where the object is placed at or near the focal point of the lens, allowing the viewer to look through the magnifying glass without straining their eyes. The script explains that with relaxed vision, the magnification can be calculated as 25 divided by the focal length.
๐Ÿ’กStrain vision
Strain vision is when the object is placed closer to the lens than the focal point, resulting in a larger image formed at a closer distance. The script mentions that looking at the image with strain vision provides a larger magnification angle, and the magnification is calculated differently than with relaxed vision.
๐Ÿ’กLens equation
The lens equation relates the object distance (s), the image distance (s'), and the focal length (F) of a lens. The script briefly mentions the lens equation when discussing the conditions under which the object should be placed to achieve a certain image distance and magnification.
๐Ÿ’กObject distance
Object distance is the distance between the object and the lens. In the script, adjusting the object distance changes the image distance and thus the magnification. The video explains how to calculate the new object distance to achieve a specific image distance of 25 centimeters for strain vision.
Highlights

Introduction to the lecture on optical instruments, starting with the magnifying glass.

Explanation of how a magnifying glass works by altering the angular size of an object.

The concept of angular size as the ratio of object height to the distance from the observer.

The effect of placing an object at the focal length of a magnifying glass to create a virtual image.

Relaxed vision through a magnifying glass and its impact on the perceived size of the image.

Calculation of magnification as the ratio of the new angular size to the original.

Use of tangent function to relate the object height and distances in the magnification process.

Approximation of tangent for small angles to simplify the magnification calculation.

Derivation of the magnification formula as 25 divided by the focal length of the lens.

Example calculation for a magnifying glass with a 10-centimeter focal length, resulting in 2.5x magnification.

Difference between relaxed vision and strain vision when using a magnifying glass.

How to adjust the object's distance from the lens to change the image distance and magnification.

Equation for the object distance to achieve a specific image distance with a magnifying glass.

General formula for magnification when using strain vision and its derivation.

Final magnification formula incorporating the focal length and desired image distance.

Practical application of the magnification formula for different viewing conditions.

Summary of the key points for determining magnification with a magnifying glass.

Transcripts

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Optical InstrumentsMagnificationScienceEducationLectureVisionFocal LengthVirtual ImageRelaxed VisionStrain Vision