Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics. The Ray Model of Light

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence. Reflection; Image Formation by a Plane Mirror

Law of Reflection 1 A B Mirror

Fermat’s Principle Using Fermat’s Principle you can prove the Reflection law. It states that the path taken by light when traveling from one point to another is the path that takes the shortest time compared to nearby paths. JAVA APPLET Show Fermat’s principle simulator

Two light rays 1 and 2 taking different paths between points A and B and reflecting off a vertical mirror 1 2 A B Plane Mirror Use calculus - method of minimization

Write down time as a function of y and set the derivative to 0.

When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection. Reflection; Image Formation by a Plane Mirror

With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position. Reflection; Image Formation by a Plane Mirror

Example 32-1: Reflection from flat mirrors. Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 15° with the first mirror as shown. What angle will the outgoing beam make with the second mirror?

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror. This is called a virtual image, as the light does not go through it. The distance of the image from the mirror is equal to the distance of the object from the mirror. Reflection; Image Formation by a Plane Mirror

Example : How tall must a full-length mirror be? A woman 1.60 m tall stands in front of a vertical plane mirror. What is the minimum height of the mirror, and how close must its lower edge be to the floor, if she is to be able to see her whole body? Assume her eyes are 10 cm below the top of her head.

ConcepTest 32.1Reflection When watching the Moon over the ocean, you often see a long streak of light on the surface of the water. This occurs because: 1) the Moon is very large 2) atmospheric conditions are just right 3) the ocean is calm 4) the ocean is wavy 5) motion of the Moon

angle of incidence also changesdifferent spots on the water can reflect the Mooninto your eyes at different times When the water surface changes, the angle of incidence also changes. Thus, different spots on the water can reflect the Moon into your eyes at different times. ConcepTest 32.1Reflection When watching the Moon over the ocean, you often see a long streak of light on the surface of the water. This occurs because: 1) the Moon is very large 2) atmospheric conditions are just right 3) the ocean is calm 4) the ocean is wavy 5) motion of the Moon Follow-up: Where else does this occur?

ConcepTest 32.2aMirror I S O mirror An observer at point O is facing a mirror and observes a light source S. Where does the observer perceive the mirror image of the source to be located?

ConcepTest 32.2aMirror I S O mirror Trace the light rays from the object to the mirror to the eye. Since the brain assumes that light travels in a straight line, simply extend the rays back behind the mirror to locate the image. An observer at point O is facing a mirror and observes a light source S. Where does the observer perceive the mirror image of the source to be located? Follow-up: What happens when the observer starts moving toward the mirror? toward the mirror?

ConcepTest 32.2bMirror II You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely? 1) same as your height 2) less than your full height but more than half your height 3) half your height 4) less than half your height 5) any size will do

ConcepTest 32.2bMirror II  i =  r mirror only half your size Trace the light rays from the image’s foot to the mirror and then to the eye. Since we know that  i =  r, you need a mirror only half your size. You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely? 1) same as your height 2) less than your full height but more than half your height 3) half your height 4) less than half your height 5) any size will do

ConcepTest 32.2cMirror III Does this depend on your distance from the mirror? 1) no 2) yes 3) depends on the mirror 4) depends on the person

ConcepTest 32.2cMirror III Does this depend on your distance from the mirror? The farther you step back, the smaller the incident and reflected angles will be. But the rays will still be reflected at the same points, so the ray from the foot will still be reflected at mid- height. 1) no 2) yes 3) depends on the mirror 4) depends on the person

ConcepTest 32.3All Smoke and Mirrors 1.0 m 0.5 m 1) 0.5 m 2) 1.0 m 3) 1.5 m 4) 2.0 m 5) 2.5 m You hold a hand mirror 0.5 m in front of you and look at your reflection in a full-length mirror 1 m behind you. How far in back of the big mirror do you see the image of your face?

small mirror0.5 m big mirror2.0 m 2.0 mbig mirror The image of the face reflected in the small mirror appears 0.5 m behind the small mirror. This image (which is the object for the big mirror) is 2.0 m away from the big mirror. The final image is 2.0 m behind the big mirror. ConcepTest 32.3All Smoke and Mirrors 1.0 m 0.5 m 1) 0.5 m 2) 1.0 m 3) 1.5 m 4) 2.0 m 5) 2.5 m You hold a hand mirror 0.5 m in front of you and look at your reflection in a full-length mirror 1 m behind you. How far in back of the big mirror do you see the image of your face?