Optics: Lenses & Mirrors

Thin Lenses Thin Lenses: Any device which concentrates or disperses

light.

Types of Lenses:

A. Converging Lens: Parallel rays of light are concentrated at a point called the principal focus. Shape: convex

All distances measured from the origin. The light bends because of refraction.

The focal length is the distance at which sunlight is concentrated at the burning point.

B. Diverging Lens: Parallel light is dispersed as if it had come from the focus. Shape: concave

Solid lines are actual light paths.

Dashed lines are where we thing the light travels because our brain things that light travels in straight lines.

Converging LensesA. f (+) = Focal Distance

p (+) = object location

q = image location

q (+) = real, inverted image. The light rays actually intersect. We can view these images on a screen, record them on film or detect them on our retina.

q (-) = virtual, upright image. The light rays do not actually intersect. We cannot view them on a screen. They exist only in our mind.

B. Formulas:

€

1

f=1

p+1

q

€

Magnification,M =q

p

€

Height :H image = M ∗Hobject

Ex: A candle, 12 cm tall, stands 60 cm from a converging lens, whose focal length is 20 cm.

Find the location and nature of the image.

Find the magnification and the size of the image.

Cartoon: Center ray straight. Horizontal ray bends through f.

Ex: A candle, 72 cm tall, stands 45 cm from a converging lens whose focal length is 180 cm.

Find the location and nature of the image.

Find the magnification and the size of the image.

Cartoon:

Ex: Given: p = 80 f = 80 Find q.

Diverging Lenses Parallel light is dispersed as if it had come from the focus.

A. f (-) = Focal Distance

p (+) = object location

q (-) = image location

Note: For all diverging lenses, regardless of the object location, the image location, q, will always be (-). Therefore, the image will always be virtual and upright. We cannot view these images on a screen. They only exist in our mind, since the light rays do not actually intersect.

B. Formulas:

€

1

f=1

p+1

q

€

Magnification,M =q

p

€

Height :H image = M ∗Hobject

Ex: A candle, 12 cm tall, stands 60 cm from a diverging lens, whose focal length is -30 cm.

Find the location and nature of the image.

Find the size of the image.

Cartoon:

Summary

A. Type of Lens

f = (+) converging

f = (-) diverging

B. Object Location

p = (+) always

C. Image Location

q = (+) real, inverted

q = (-) virtual, upright

€

1

f=1

p+1

q

€

M =q

p

€

H image = M ∗Hobject

Structure of the Eye1. Cornea: Focuses light due to curvature and slowing.

2. Lens: Variable power due to changing its shape. The lens allows us to focus at various distances.

3. Retina: Analogous to film. A real, inverted image is formed on the retina. Rods and cones detect this image and send a signal to the brain.

Vision in a normal eye:

Spherical Mirrors The light rays follow the law of reflection: θ1 = θ2

Types of Mirrors:

A. Converging: f = (+). Parallel light is concentrated at the principal focus.

B. Diverging: f = (-). Parallel light is dispersed as if it had come from the conjugate focus.

Plane Mirror

Cartoon: Object and image are same size. Our depth perception gets distance correct, but our brain thinks light travels in straight lines.