The Thin Lens Equation

The Thin Lens Equation•Let’s us predict mathematically the

properties of an image produced by a lens

Defining Variables•f = focal length, distance from the focus to the optical centre (F and F’ are the same distance from O).

•do = distance from the object to the optical centre

•di = distance from the image to the optical centre

•ho = height of the object•hi = height of the image

The Thin Lens Equation

fdd io

111

Sign Conventions•Object distances (do) are always positive.

•Image distances (di) are positive for real images and negative for virtual images.

•The focal length (f) is positive for converging lenses and negative for diverging lenses.

To rearrange the equation, you need 3 basic math skills:

1. Cross the line, change the sign. To move a term to the other side of an equal sign; switch the “+” or “-”.

2. How to cross multiply, if it is on the top; then on the other side it is on the bottom and vice versa.

3. How to inverse an equation; basically you put a one over it as the one becomes the top half of a fraction.

Example 1:A converging lens has a focal length of 25 cm. A light bulb is 60 cm away from the lens. Where will the image be formed?

•Ans: di = +43 cm

Example 2:•A diverging lens has a focal length of 30 cm. A flower is placed 20 cm away from the lens. Where will the image be formed?

•Ans: di = -12cm

Copy Table 1, Pg 566 into your notes

Homework•Pg 566 # 1-4

The Magnification Equation

The Magnification Equation

o

i

o

i

dd

hhM

Where M = magnification of the imageMagnification has no units as they will cancel out.

Sign Conventions•Object height (ho) and image height (hi) are positive when measured upward from the principal axis (PA) and negative when measured downward.

•Magnification (M) is positive for an upright image and negative for an inverted image.

Example 1:An Ipod has a height of 11cm is balanced in front of a converging lens. An upright, virtual image is noticed with a height of 17 cm occurs on the same side. What is the magnification of the lens?

Example 2:•An Ipod has a height of 11cm is balanced in front of a converging lens. An inverted, real image is noticed with a height of 38.5 cm on the opposite. What is the magnification of the lens?

Example 3:A toy rocket is placed 12 cm away from a diverging lens. An upright, virtual image image is noticed 9.0cm on the same side as the rocket. What is the magnification of the lens?

Homework•Pg 566 # 5-8