Lenses

Lenses• A converging lens, or positive lens is a convex lens.• A diverging lens, or negative lens is a concave lens.• We will be using biconvex lenses for IB.• Lenses use refraction, and the rays bend twice in

the lens.• We simplify this by bending light rays once along a

vertical line at the lens midpoint.• We refer to lenses as “thin” lenses so we can

simplify by bending the rays once.

Biconvex Lens• This lens is called a converging lens (or positive

lens).• Light rays converge on the real side (right side) at

the focal point.• As it is composed of two circular objects joined

together, there are two foci.• The real focus is on the right side and the virtual

focus is on the left side.• Uses: Magnifying glasses, cameras, photographic

enlargers, slide projectors, movie projectors, reading glasses.

Biconvex Lens• The centre of the lens, where it meets the principal

axis (PA), is called the optical centre (OC)• The vertical line bisecting the lens is called the axis

of symmetry (A of S)• There are two focal points: the real one (F) and the

virtual one (F’).• Light rays parallel to the principal axis, will converge

at the focal length, f.

FF’ OC

A of S

PA

Biconvex Lens

• A thin lens has a thickness much smaller than f.• Three rays are used, to locate images. • Ray 1: a ray parallel to PA from the top of the object

to the A of S, refracts through F• Ray 2: a ray passing through F’ and the top of the

object to the A of S, refracts parallel to the PA• Ray 3: a ray passing through the OC to the A of S,

will not refract and will pass straight through

Biconvex Lens

• Ray Diagram

FF’ OC

O

Biconvex Lens

• Ray Diagram

FF’ OC

O

Biconvex Lens

• Ray Diagram

FF’ OC

O

Biconvex Lens

• Ray Diagram

FF’ OC

O

Biconvex Lens

• Ray Diagram

FF’ OC

O

Biconvex Lens

• Ray Diagram

FF’ OC

O

I

Biconvex Lens

• Ray Diagram

FF’ OC

O

IImage CharacteristicsType: RealAttitude: InvertedMagnification: M = hi/ho = - _____cm/ ______cm = - ______Location: di = + ________ cm

Human Eye

Calculations• We can use the mirror formulae with lenses again.• The thin lens equation is very applicable here

(obviously!)• Remember that di is negative for virtual images and

hi is negative if the image is inverted.

o

i

o

i

d

d

h

hM

io ddf

111

Calculations• Ex 1) A convex lens of a magnifying glass is held 2.00

cm above a page to magnify the print. If the image produced by the lens is 3.60 cm away and virtual, what is the focal length of the lens?

io ddf

111

cmcmf 60.3

1

00.2

11

cmf

222.01

cmf 50.4

Calculations• Ex 2) A convex lens has a focal length of 60.0 cm. A

candle is placed 50.0 cm from the lens. What type of image is formed and how far is the image from the lens?

io ddf

111

idcmcm

1

0.50

1

0.60

1

cmxdi21000.3

idcmcm

1

0.50

1

0.60

1

cmdi

003333.01

As di is negative, the image is virtual.

Text Practice

Note: A biconcave lens is not required for SL.Page 739 #5, 6 – 9, 13.Page 740 #22 – 28

Lens worksheet