The Thin Lens Equation. Let’s us predict mathematically the properties of an image produced by a lens.

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Presentation transcript:

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). d o = distance from the object to the optical centre d i = distance from the image to the optical centre h o = height of the object h i = height of the image

The Thin Lens Equation

Sign Conventions Object distances (d o ) are always positive. Image distances (d i ) 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: d i = +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: d i = -12cm

Copy Table 1, Pg 566 into your notes

Homework Pg 566 # 1-4

The Magnification Equation

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

Sign Conventions Object height (h o ) and image height (h i ) 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