LECTURE 10MIRRORS, LENSES & IMAGES

Instructor: Kazumi Tolich

Lecture 10

¨ Reading chapter 32-1 to 32-2¤ Mirrors

n Plane mirrorsn Concave and convex spherical mirrors

¤ Lensesn Refractionn Thin lenses

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Plane mirrors¨ We will denote:

¤ s: the distance between the mirror and the object¤ s’: the distance between the mirror and the image¤ y: the height the the object¤ y’: the height of the image

¨ The reflected rays diverge as if they came from point P’ (image of the object at P).

¨ This image at P' is called a virtual image because the light does not really come from it.

¨ The object distance s and the image distance s’ are equal.

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Left/right reflection?

¨ Paradox: Why does a mirror reverse left and right when it does not reverse up and down?

¨ Answer: A mirror reverses neither left and right nor up and down. It reverses front and back. This has the effect of making a left hand into a right hand, and vice versa. This is called depth inversion.

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Concave and Convex spherical mirrors

¨ Concave mirrors look like a cave looking into the mirror.¤ Rays from P reflecting off a concave mirror converge at P’.

¨ Convex mirror looks opposite.¤ The reflected rays appear to come from a point behind the mirror.

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Concave Convex

Real vs. virtual images

¨ An image is called a real image if light really comes from the image point.¨ An image is called a virtual image if light does not really come from the

image point.

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Real Virtual

Mirror equation

¨ We assume that the rays reflects off only a small part of the spherical surface.¨ The mirror equation gives the relationship among the radius of the curvature r, the

focal length f, the object distance s, and the image distance s’.

¨ The lateral magnification, m, is defined to be

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y

s r

Sign conventions for reflection

¨ s is positive if the object is on the incident-light side of the mirror.

¨ s’ is positive if the image is on the reflected-light side of the mirror.¨ r and f are positive for a concave mirror, and negative for a convex mirror.

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Incident-light & Reflected-light side

Quiz: 19

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Ray diagram for mirrors

¨ Constructing the image point by using principal rays:

1. The “parallel ray,” drawn parallel to the axis, is reflected through F.

2. The “focal ray,” drawn through F, is reflected parallel to the axis.

3. The “radial ray,” drawn through the center of the curvature (C), is reflected back along the radius.

¨ The image is at the cross point.

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V

V

V

Make-up/shaving mirror

¨ When you place your face near a spherical concave mirror, inside its focal point, the image of your face is magnified and upright.

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Your face here. Your face image here.

V

Quiz: 212

Example 1

¨ A convex mirror has a radius of curvature that has a magnitude equal to 24 cm. Locate the image for an object near the axis at distance of 12 cm from the mirror. Is the image real or virtual; upright or inverted; and enlarged, reduced, or the same size as the object?

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Demo 2

¨ Large Concave Mirror: ¤ Strawberry and Candle Burning at Both Ends

n Demonstration of object placed outside of the focal point, forming a real inverted image.

¤ One Candle Searchlightn Demonstration of object placed at the focal plane of the mirror throwing a roughly parallel beam to

the far wall.

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Image due to refraction

¨ Relationship among the image distance s’, the object distance s, the radius of the curvature of the surface r, and indices of refraction n1 and n2 is given by

¨ The magnification due to refraction at a spherical surface:

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Incident-light side Refracted-light side

Sign convention for refraction

¨ s is positive for objects on the incident-light side of the surface.¨ s’ is positive for images on the refracted-light side of the surface.¨ r is positive if the center of curvature is on the refracted-light side.

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Example 2

¨ A very long 1.75-cm-diameter glass rod has one end ground and polished to a convex spherical surface that has a 7.20-cm radius. The glass material has an index of refraction of 1.68. A point object in air is on the axis of the rod and 30.0 cm from the spherical surface. Find the location of the image and state whether the image is real or virtual.

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(f > 0) (f < 0)

Converging and diverging thin lenses

¨ When parallel rays pass through:¤ a converging (positive) lens: the rays converge at f.¤ a diverging (negative) lens: the rays diverge away from f.

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Focal points

¨ Lenses have two focal points, one on each side.¤ For a converging lens: the first focal point is on the incident-light side and the

second focal point is on the refracted-light side.¤ For a diverging lens: the opposite is true.

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1st 2nd

Thin lenses

¨ Refraction occurs at each surface of a thin lens.

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This is the same as the mirror eqn.But this has the different sign conventions.

Magnification by a lens

¨ The lateral magnification by a lens is given by

¤ a positive magnification indicates that the image is upright.

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Power of a lens

¨ The power of a lens is defined to be

¨ The unit is diopters (D) when f is given in meters.¨ Measure of lens’ ability to focus parallel light at a short distance from

the lens.¨ Diverging lens’ power is negative.

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Ray diagram for thin lenses

¨ Constructing the image point by using principal rays:a) The parallel ray, drawn parallel to the axis emerges directed toward the second focal point.

b) The focal ray, drawn through the first focal point emerges parallel to the axis. c) The central ray, drawn through the center of the lens, is undeflected.

¨ The image is at the cross point.

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2nd focal point 1st focal point

Quiz: 3

Demo 3

¨ Image Formation¤ Demonstration of a double convex lens forming an inverted and magnified

image.

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Example 3

¨ A plano-convex lens is made of glass having an index of refraction of 1.5. The radius of curvature of the lens is 20.0 cm.

a) Find the focal length of the lens.b) If an object is placed 40.0 cm in front

of the lens, where will the image be located?

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