Warm-Up 1.  A light ray is passing through water (n=1.33)

towards the boundary with a transparent solid at an angle of 56.4°. The light refracts into the solid at an angle of refraction of 42.1°. Determine the index of refraction of the unknown solid.

2.  Light in air approaches the boundary of oil at an angle of 36.1 degrees with respect to the normal. The light travels at a speed of 2.27 x 108 m/s through the oil. Determine the angle of refraction.

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 Lenses A.  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:

€

1f

=1p

+1q

€

Magnification,M =qp

€

Height :Himage = 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:

Warm-Up During a lens lab, Jerome and Michael placed a 4.5 cm tall night light bulb a distance of 42.8 cm from a lens. The image of the light bulb was inverted and appeared 26.5 cm from the lens.

A.  Determine the focal length of the lens being by Jerome and Michael.

B.  Determine the expected height of the image of the bulb.

C.  Draw a ray diagram for this situation. Are your answers consistent?

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:

€

1f

=1p

+1q

€

Magnification,M =qp

€

Height :Himage = 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

€

1f

=1p

+1q

€

M =qp

€

Himage = M ∗Hobject

Structure of the Eye 1.  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:

Eyes & Vision A.  Power of lenses

Power = 1/f = [1/meters = Diopters]

B.  Intuitions: Lenses with lots of power bend light rays sharply. Lenses with lot of curvature and which slow down the light a lot have lots of power.

C.  Power is additive. Focal length is not additive.

Ex: Given:

f1=.75 m

f2=-.25 m

Find the individual power of each lens and the total power of the two lenses combined.

Vision Vision in a normal eye:

Eye diameter = 1.7 cm = q

1.  Far vision – find the power to focus at infinity.

2.  Near vision – find the closest point at which we can comfortably focus.

Definitions

1.  Near point = closest distance at which we can comfortably focus. Normal eye = 25 cm.

2.  Far point = furthest distance at which we can focus. Normal eye = infinity.

3.  Myopia = near sighted. Can’t focus at infinity. Cause: elongated eyeball.

4.  Hypermetropia = far sighted. Can’t focus close up. Cause: short eyeball.

5.  Presbyopia = eye can focus only at limited, intermediate distances. Cause: “loss of lens accommodation.” The old lens loses its flexibility and cannot change its shape to focus at various distances.

Prescribing Glasses Key: We want to make a virtual, upright image in the visible zone.

Thus, for glasses, q = (-).

Ex: Miss Stein’s visible zone is from 50 cm to 2.5 m. Find glasses so that she can see a book held at 20 cm and a mountain at infinity.

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.

Formulas:

  Converging mirrors:

A.  f = focal length = (+)

p = object location = (+)

q = image location

q = (+) real, inverted; light rays actually intersect

q = (-) virtual, upright; light rays do not actually intersect – image only exists in our minds.

Ex: Given: f = 30, p = 120. Find location and nature of the image.

€

1f

=1p

+1q

€

M =qp

€

Himage = M ∗Hobject

€

R = 2 f

Ex: Given f = 48, p = 12. Find location and nature of image.

Ex: Given f = 45, p = 45. Find location and nature of image.

Ex: Given p = 100 and magnification = 5. Image is virtual and upright. Find radius of the mirror.

Diverging Mirrors

  Diverging Mirrors:

A.  f = focal length = (-)

p = object location = (+)

q = image location = (-)

Diverging mirrors only make virtual, upright images.

Ex: A diverging mirror has radius 100 cm. An object has magnification 0.4 to make a smaller, upright image. Find the object and the image location.

Plane Mirror

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