Part 1 /2

High School Optics

by SSL Technologies

Physics Ex-52

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LENSES

Whereas mirrors produce images by reflection, lenses produceimages by refraction. Depending upon their “thickness”, lensesare classified as “thick” or “thin”. In this course, we will onlyconsider “thin” lenses. In effect, therefore, we disregard thethickness of the lens assuming it to be a line.

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Convex

Concave

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There are two main types of lenses called convex (also knownas converging ) and concave (also known as diverging ).

Convex lenses are thicker in the middle than at the edges whileconcave lenses are thicker at the edges than in the middle.

As illustrated below, both convex and concave lenses each havethree variations.

PART-1

Physics Ex-52

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When representing “thin” lenses in a diagram, it is sometimes moreconvenient to simply draw an arrow rather than the actual lens.

Using this method, an arrow is used to represent the lens asillustrated below.

PART-1

Convex Lens Concave Lens

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Convex lenses are thicker in the middle and thus converge

light rays.

Concave lenses are thinner in the middle and thus diverge

light rays.

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Just as with concave mirrors, the characteristics of the imageformed by a converging lens depend upon the location of the object.

There are six "strategic" locations where an object may be placed.For each location, the image will be formed at a different place andwith different characteristics. We will illustrate the six differentlocations and label them as CASE-1 to CASE-6.

PART-1

Case-1: Object at infinityCase-2: Object just beyond 2 F’Case-3: Object at 2F’Case-4: Object between 2F’ and F’

Case-5: Object at F’Case-6: Object within focal length (f)

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CASE-1 : Object at “infinity”

No image formed (All rays pass through F)

No image

NOTESince the object is at “infinity”,

all rays arrive parallel.

Infinity simply means “far away”.

Object

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CASE-2 : Object just beyond 2F’

Image is real (formed by refracted rays)

Inverted (upside down)

Reduced (smaller than object)

Located between F and 2F

Object Image

Note-1A ray that comes parallel

is refracted through F.

Note-2A ray that goes through thevertex goes right through.

Note-3A ray that goes through F’

is refracted parallel.

NOTEIn order to establishan image point, allwe need are twointersecting rays.

This ray is extrain locating the

image.

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CASE-3 : Object at 2F’

Image is real (formed by refracted rays)

Inverted (upside down)

Same size as objectLocated at 2F

Object Image

Again:In order to establishan image point, allwe need are twointersecting rays.

This ray is extra.

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CASE-4 : Object between 2F’ and F’

Image is real (formed by refracted rays)

Inverted (upside down)

Magnified (larger than object)

Located beyond 2F

Object Image

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CASE-5 : Object at F’

No image is formed (rays refract parallel)

Object No image

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CASE-6 : Object is within focal length

Image is virtual (formed by extended rays)

UprightMagnifiedLocated on same side as object

Object

Image

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One case only!

Image is always virtual (formed by a direct ray and an extended ray)

Always uprightAlways reducedAlways located on same side as object

Object

Image

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Sign convention:

1- Object distance is always positive.

2- Image distance is positive if the image is on the side of the lens where light emerges (from lens).

3- Image distance is negative if the image is on the side of the lens where the light enters (the lens).

4- The focal length of a convex (converging) lens is positive.

5- The focal length of a concave (diverging) lens is negative.

PART-1

Be sure to follow the following sign convention whensolving problems concerning lenses.

Physics Ex-52Question-1

A lens that is thicker in the middle than at the ends is known as:

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A lens or a lens. Convex Converging

Physics Ex-52Question-2

A lens that is thicker at the ends than in the middle is known as:

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A lens or a lens. Concave Diverging

Physics Ex-52Question-3

Trace the rays that emerge from the following glass mediums:

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a)

b)

c)

d)

Physics Ex-52Question-4

For each case below, draw the appropriate lens that will producethe indicated rays.

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a)

b)

Convex (converging)

Concave (diverging)

Physics Ex-52Question-5

How is the image formed by a mirror different from the imageformed by a lens?

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A mirror forms an image by reflection whereasa lens forms a an image by refraction.

Physics Ex-52Question-6

For each convex lens illustrated below, draw the image.

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a)

Image

Image is real, inverted, reducedand located between F and 2F.

Physics Ex-52Question-6

For each convex lens illustrated below, draw the image.

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b)

Image

Image is real, inverted, samesize object and located at 2F.

Physics Ex-52Question-6

For each convex lens illustrated below, draw the image.

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c)

Image

Image is real, inverted, magnifiedand located beyond 2F.

Physics Ex-52Question-6

For each convex lens illustrated below, draw the image.

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d)

Parallel

All rays refract parallel,no image is formed.

Physics Ex-52Question-6

For each convex lens illustrated below, draw the image.

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e)

Image

Image is virtual, upright, magnifiedand located on same side as object.

Physics Ex-52

For each concave lens illustrated below, draw the image.

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Image

Image is virtual, upright, reducedand located on same side as object.

REMEMBER

Concave lenses always produce imagesthat are virtual, upright and reduced.

Question-7

Physics Ex-52Question-7

For each concave lens illustrated below, draw the image.

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Image

Image is virtual, upright, reducedand located on same side as object.

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Type (real or virtual): _______________

Location: _______________

Magnification: _______________

Height: _______________

Question-8

An object that is 7 cm high is placed 20 cm in front of a convex (converging) lens whose focal length is 15 cm. Determine thecharacteristics of the image:

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Real

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60 cm

- 3 (inverted and 3x larger than object)

21 cm

Negative sign indicates inversion.

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Type (real or virtual): _______________

Location: _______________

Magnification: _______________

Height: _______________

Question-9

An object whose height is 4 cm is placed 50 cm from a concave (diverging) lens. If the focal length of the lens is 30 cm, determinethe characteristics of the image:

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Virtual

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18.75 cm

0.375 (upright and smaller than object)

1.5 cm

Note that diverging lenseshave a negative focal length.

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Type (real or virtual): _______________

Location: _______________

Magnification: _______________

Height: _______________

Question-10

An object that is 5 cm high is placed 70 cm in front of a convex (converging) lens whose focal length is 20 cm. Determinethe characteristics of the image:

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Real

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28 cm

- 0.04 (inverted and smaller than object)

2 cm

Negative sign indicates inversion.

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A lens produces the following optical effect.

Which group of lens produces the above effect?

Question-11

Plano convexPlano convexD)D)

Double convexDouble convexC)C)

Plano concavePlano concaveB)B)

Double concaveDouble concaveA)A)

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Beams of light rays are traveling through air parallel to theprincipal axis of four different lenses. The light rays enterthe lenses and are refracted.

In which diagram are the light rays correctly illustrated?

Question-12

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