Curved Mirrors and Thin Lenses

Links and useful resources

Lightning Round Questions

What is snell's law?
What's the difference between a real image and a virtual image?
You look into a mirror and see yourself. Is it a real image or a virtual image?
When does a switch in a circuit need a pull-up or pull-down resistor, and when do you not need one at all?
What is the formula for the gravitational force of attraction between any two masses?
How much gravitational potential energy does a 10 kg mass have if it is 20 meters above the ground?

gr7: [lightning:: 3]
gr10: [lightning:: 2]

Lesson content with examples

focal length for curved mirrors
focal length for lenses
Magnification
object distance vs image distance
Thin lens equation

Magnification

There are two kinds of magnification we'll be looking at:

Lateral magnification
Angular magnification

Lateral magnification is the ratio of the size of the image to the size of the object. Angular magnification is the ratio of the angle subtended by the image to that of the object.

Magnification is a slightly misleading term - in common use, it means making something appear larger. In physics, it means simple making something appear with a different size - it could be smaller!

Compute magnification like this:

magnification (m) = - \frac{s^{'}}{s}

where $s^{'}$ is the distance of the image from the lens, and $s$ is the distance of the object itself.

The sign of the result tells you whether the image is inverted or upright: negative results mean an inverted image
The magnitude of the result tells you the relative size of the image: Multiply the size of the object by the magnification to get the size of the image.
The image distance $s^{'}$ is defined to be a negative number for a virtual image, and postive for a real image.

Thin Lens Equation

This is the thin lens equation - it lets you compute the object distance ( $s$ ), the image distance ( $s^{'}$ ) or the focal length $f$ of a lens if you know the other two:

\frac{1}{s} + \frac{1}{s^{'}} = \frac{1}{f}

The focal length of a thin lens can be computed if you know the index of refraction (n) and the radius of each side of the lens ( $R_{1}, R_{2}$ ):

\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})

All of the terms have sign conventions that tell you when the term should be positive or negative depending on the situation:

Term	Positive when	Negative When
$R_{1}, R_{2}$	Convex toward the object	Concave toward the object
f	Converging lens, thicker in the center	Diverging lens, thinner at the center
$s^{'}$	Real image, opposite side from object	Virtual image, same side as object

Curved mirrors

The mirror equation for curved mirrors is identical to the thin lens equation!

\frac{1}{s} + \frac{1}{s^{'}} = \frac{1}{f}

Mirrors can also make real or virtual images. In a concave mirror, a real image is made on the same side of the mirror as the object. In a convex mirror, a virtual image is made on the opposite side of the mirror from the object.

Examples

What is the focal length of a meniscus lens (a lens with curves that bend in the same direction) where $R_{1} = 40 c m$ and $R_{2} = 20 c m$ ?
A magnifying lens is 2.0 cm above a stamp. The magnification is 4.0. What is the focal length of the lens?
Let's compute the focal lengths of our magnifying glasses. How could we do that?

Checking homework

Dataview: No results to show for task query.

Guided practice

A 4.0 cm diameter flower is 200 cm from the 50 cm focal length lens of a camera. How far should the light detector be placed behind the lens to record a well-focused image? What is the diameter of the image on the detector?
You are holding a magnifying lens with a 6.0 cm focal length 4.0 cm above a flower in order to magnify it. What is the magnification?

Homework

What is the magnification when you use a lens with 8 cm focal length to view something at a distance of 7 cm? 2025-04-09
should you move the lens closer or farther from the object if you want to increase the magnification? 2025-04-09
What happens to the image you see if you move the lens past the focal point? 2025-04-09

#hw (physics) Three problems, see the lesson page under "Homework" 2025-04-09