Sign of the magnification
A minus sign means real. A plus sign means virtual.
Minus or plus?
A mirror gives a real, upside down image of a flame, and another mirror gives a virtual, upright image of it. A student works out m = h′/h for both and gets one answer with a minus sign.
Which image do you think has the minus sign?
What this lesson covers
The idea
Object height is taken as positive; image height is positive for virtual and negative for real images, so a negative magnification means a real image and a positive one a virtual image.
Minus or plus?
A mirror gives a real, upside down image of a flame, and another mirror gives a virtual, upright image of it. A student works out m = h′/h for both and gets one answer with a minus sign.
Which image do you think has the minus sign?
- The real one
- The virtual one
- Neither: m never has a sign
Read the signs
In each picture look at the signs of h′ and m. Open every tab.
The sign tells the kind
In the real image the height h′ was negative, so m was negative. In the two virtual images h′ was positive, so m was positive.
The height of the object is taken as positive. The height of the image is positive for virtual images and negative for real images. So a negative magnification means a real image and a positive magnification means a virtual image.
Notes
Object height is positive. The image height is positive if virtual, negative if real. So m is negative for a real image and positive for a virtual image.
Check yourself
A mirror has magnification m = −2. The image is
What sign is given to the height h′ of a virtual image?
An object is 1.5 cm tall (h = +1.5 cm). A mirror forms a real image with h′ = −3.0 cm. What is m = h′/h?
Answer: -2
m = h′/h = (−3.0 cm)/(+1.5 cm) = −2.
A convex mirror has m = +0.23. What is the image like?
- real — correct. Yes!
- virtual. A positive magnification means a virtual image. A negative one means a real image.
- neither real nor virtual. Every image is either real or virtual. The negative sign shows it is real.
- Negative. Negative is used for the height of a real image.
- Positive — correct. Yes!
- No sign is used. The height of the image is given a sign: positive for a virtual image and negative for a real image.
- Real, inverted and smaller than the object. A real image has a negative magnification. This one is positive, so the image is virtual and erect.
- Virtual, erect and larger than the object. The size of m is 0.23, which is less than 1, so the image is smaller than the object.
- Virtual, erect and smaller than the object — correct. Yes!