Lenses & MirrorsCh 18

A plane mirror

• A flat, smooth surface where light is reflected by regular reflection.

• Image formed by brain where all rays would have met if they were straight (in mirror)

Concave Mirror

• Flashlights and headlights• Curves inward- concave(metal spoon)*Gather light, rays intersect

that is the focal point (light straight on center)

Distance between center of mirror and focal pt is the focal length.

2 rules:1)Ray of principle axis passes focal pt2)Ray through focal is parallel to principle axis

How to determine the focal point

To find focal point (F) you will need to find the focal length(f) . It is half the radius of curvature of the mirror or 2f=r. If mirror has a radius of curvature of 10.0 cm than the f=5cm from the center of the mirror

How to draw ray diagram

Image produced depends on the position of the object in relation to the

focal point.

Images- It depends where the object is located in reference to the mirror and focal point.

• 1) Objects will appear as a virtual image if in FRONT of focal pt (behind the mirror)

• 2) a small inverted image• 3) a large inverted image

Lens/Mirror Equation

• f=focal length of the mirror

• do (p)=distance from object to mirror

• di=(q)distance from image to mirror

• M=magnification• h=height

Calculating a Real Image formed by a concave mirror

• A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a radius of curvature of 30.4 cm. Determine the image distance and the image size.

• ho = 4.0 cm f= 30.4/2= 15.2cm• do = 45.7 cm• f = 15.2 cm

• 1/f = 1/do + 1/di 1/(15.2 cm) = 1/(45.7 cm) + 1/di

• 0.0658 cm-1 = 0.0219 cm-1 + 1/di

• 0.0439 cm-1 = 1/di

• di = 22.8 cm

Now find the height

• hi/ho = - di/do mag. Equation

• hi /(4.0 cm) = - (22.8 cm)/(45.7 cm)

• hi = - (4.0 cm) • (22.8 cm)/(45.7 cm)

• hi = -1.99 cm (neg so inverted)

Why are some things + and - ?• f is + if the mirror is a concave mirror • f is - if the mirror is a convex mirror • di is + if the image is a real image and located on

the object's side of the mirror. • di is - if the image is a virtual image and located

behind the mirror. • hi is + if the image is an upright image (and

therefore, also virtual) • hi is - if the image an inverted image (and

therefore, also real

What about Lenses?

• A lens is called convex if it is thicker at the center than at the edges

• A lens is called concave if it is thinner at the middle than at the edges

Convex or Concave

Focusing with Lenses

Focal Length=distance from the lens to the focusFocus= point the light converges

Focusing with Lenses

Real or Virtual

Real – rays converge on back side of lens

Virtual – rays diverge on backside of lens

Problem

• A 3.0 cm high object is placed 32.0 cm from a convex lens that has a focal length of 8.0 cmWhere is the image?How high is the image?

Answer

• 1/f = 1/do + 1/di 1/(8.0 cm) = 1/(32.0 cm) + 1/di

• 0.125 cm-1 = 0.03125 cm-1 + 1/di

• 0.0935 cm-1 = 1/di

• di = 11cm ( positive so image is real)

• hi/ho = - di/do

• hi /(3.0 cm) = - 11cm)/(32 cm)

• hi = (3.0 cm) • - (11cm)/(32 cm)

• hi = -1.0 cm (neg so image is inverted)