Locating Images on Curved Mirrors and the Curved Mirror Equation

Last day in class we looked at locating images on converging and diverging mirrors.

Converging Mirror

• the image is in front of the mirror and is between C and F
• the imge is real
• the image is inverted
• the image is smaller

Diverging Mirror

• the image is behind the mirror
• the image is virtual
• the image is upright
• the image is smaller

Note: Some rays near the edge of a spherical converging mirror may not be reflected right through the principle focus. This is called spherical aberration. This can be avoided by using parabolic mirrors. When drawing ray diagrmas we should "trust" the rays closer to the middle of the mirrors.

Today in class we looked at Curved Mirror Equations

M= hi/ho=-di/do 1/di+1/do=1/f

Sign Rules:

1. All distances are measured from the vertex of the mirror
2. Real images have a positive distance
3. Virtual images have a negative distance
4. Postitive Height and Magnification= Upright
5. Negative Height and Magnification= Inverted
6. Focal length of a diverging mirror is negative

Examples

1. A candle is located 30.0 cm from a converging mirror with a radius of curvature that is 10.0 cm

a) At what distance from the mirror will the image be formed?

• do=30.0cm
• f= 10.0/2= 5.0cm ( positive because the mirror is converging)
• di=?

• 1/di+1/do= 1/f
• 1/di+1/30.0 cm= 1/5.0cm
• 1/di=1/5.0 cm- 1/30.0 cm
• 1/di= 1/6
• di= 6.0 cm

b) If the candle is 4.0cm tall, how tall will it's image be?

• ho= 4.0 cm
• hi=?

• hi/ho=-di/do
• hi/4.0cm=-6.0cm/30.0cm
• hi=4.0cm(-6.0cm)/30.0 cm
• hi= -0.80 cm (inverted)

c)What are the characteristics of the image?

• in front (di positive) between C and F
• real (di positive)
• inverted (hi negative)
• smaller (hi

2. A pencil is located 30.cm from a diverging mirror with a focal length of 20.cm

a) where will the image be located?

• do=30. cm
• f=-20. cm (negative because the mirror is diverging)

• 1/di+1/do=1/f
• 1/di+ 1/30 cm= 1/-20 cm
• 1/di=1/-20 cm - 1/30 cm
• 1/di=-1/12
• di=-12 cm

b) If the pencil is 7.0 cm tall, how tall will it's image be?

• ho=7.0 cm
• hi= ?

• hi/ho= -di/do
• hi/7.0cm= -(-12cm)/3.0 cm
• hi= (12 cm)(7.0 cm)/30 cm
• hi= 2.8 cm

c) What is the magnification of the mirror?

• M=?
• M=hi/ho = 2.8cm/7.0 cm
• M= 0.40 x

d) what are the image's characteristics?

• behind mirror (di negative) between V and F
• virtual (di negative)
• upright (hi and M poitive)
• smaller (M<1)