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33. Geometric Optics

Thin Lens And Lens Maker Equations

Physics

33. Geometric Optics

Thin Lens And Lens Maker Equations

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5:07 minutes

Problem 8

Textbook Question

How far from a converging lens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object?

Verified step by step guidance

Start by recalling the lens formula:

\frac{1}{f} = \frac{1}{d} + \frac{1}{d}

, where

f

is the focal length,

d o

is the object distance, and

d i

is the image distance.

Since the problem states that the image is real and the same size as the object, the magnification

m

is 1. Recall the magnification formula:

m = - \frac{d}{i}

. For

m = 1

, this implies

d i = d o

Substitute

d i = d o

into the lens formula:

\frac{1}{f} = \frac{1}{d} + \frac{1}{d}

, which simplifies to

\frac{1}{f} = \frac{2}{d}

Rearrange the equation to solve for

d o

d o = \frac{2}{f}

Substitute the given focal length

f = 25 cm

into the equation to find the object distance:

d o = \frac{2}{25} cm

. This gives the final object distance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Converging Lens

A converging lens, or convex lens, is a transparent optical device that bends light rays inward to a focal point. It has a positive focal length, meaning it can produce real images when objects are placed outside its focal length. Understanding how light interacts with a converging lens is crucial for solving problems related to image formation.

Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v + 1/u. This equation is essential for determining the position of the object and image in lens systems. For a real image that is the same size as the object, specific values for u and v can be derived from this formula.

Magnification

Magnification is the ratio of the height of the image to the height of the object, and it can also be expressed as the negative ratio of the image distance to the object distance (M = -v/u). For an image to be the same size as the object, the magnification must equal 1. This concept is key to understanding the conditions under which a real image can be produced at the same size as the object.

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Related Practice

Textbook Question

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of +2.0 D and +4.5 D, respectively.

(a) What maximum magnification telescope is possible?

(b) Which lens should be used as the eyepiece?

252

views

Textbook Question

Sunlight is observed to focus at a point 16.5 cm behind a lens. (a) What kind of lens is it? (b) What is its power in diopters?

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Textbook Question

A certain lens focuses an object 2.15 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?

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Textbook Question

A stamp collector uses a converging lens with focal length 28 cm to view a stamp 15 cm in front of the lens. (a) Where is the image located? (b) What is the magnification?

433

views

Textbook Question

How far apart are an object and an image formed by a 78-cm-focal-length converging lens if the image is 2.95x larger than the object and is real?

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Textbook Question

Two converging lenses are placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?

387

views

Textbook Question

An object is located 1.35 m from an 8.0-D lens. By how much does the image move if the object is moved (a) 0.90 m closer to the lens, and (b) 0.90 m farther from the lens?

268

views

Textbook Question

(II) (a) How far from a 75.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.50 x and be real? (b) What if the image is to be virtual and magnified 2.50 x?

289

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