Concave Mirror: Spherical Mirrors Where Parallel Light Rays from a Distance Source When Shined on It Are Reﬂected at a Single Point: Focal Point F

Physics 201

Professor P. Q. Hung

311B, Physics Building

Physics 201 – p. 1/31 Geometrical Optics

Physics 201 – p. 2/31 Geometrical Optics

Optics: Behaviour of Light. When the wavelength of light is much smaller than the size of the object that it interacts with, light travels approximately in a straight line ⇒ Rays. (There are exceptions!) Geometrical Optics: Study of light under the ray approximation. Provide an understanding of mirror and lenses. The eyes are an example.

Physics 201 – p. 2/31 Geometrical Optics

Some properties to be studied: Reﬂection: How light gets reﬂected at the interface between two media.

Physics 201 – p. 3/31 Geometrical Optics

Some properties to be studied: Reﬂection: How light gets reﬂected at the interface between two media. Refraction: How transmitted light changes direction at the interface between two media.

Physics 201 – p. 3/31 Wave fronts and Rays

Physics 201 – p. 4/31 Wave fronts and Rays

Physics 201 – p. 5/31 Reﬂection

For reﬂected light, one has a very simple relation: θr = θi Angle of reﬂection = Angle of incidence

Physics 201 – p. 6/31 Reﬂection

For reflected light, one has a very simple relation: θr = θi Angle of reflection = Angle of incidence Specular reflection: Reflection on smooth surface, without distortion. Metallic surfaces, for example, are good for specular reflection. (Give reasons for that).

Physics 201 – p. 6/31 Reﬂection

Physics 201 – p. 7/31 Reﬂection

Physics 201 – p. 8/31 Plane Mirrors

What are images? They are formed at the intersection of light rays, whether real or virtual.

Physics 201 – p. 9/31 Plane Mirrors

What are images? They are formed at the intersection of light rays, whether real or virtual. What’s a real image? It’s the one in which light passes through the image point.

Physics 201 – p. 9/31 Plane Mirrors

What are images? They are formed at the intersection of light rays, whether real or virtual. What’s a real image? It’s the one in which light passes through the image point. What’s a virtual image? It’s the one in which light does not pass through the image point.

Physics 201 – p. 9/31 Plane Mirrors

What about Plane Mirrors? The image is virtual.

Physics 201 – p. 10/31 Plane Mirrors

What about Plane Mirrors? The image is virtual. The image is upright, i.e. not inverted.

Physics 201 – p. 10/31 Plane Mirrors

What about Plane Mirrors? The image is virtual. The image is upright, i.e. not inverted. The image has the same size as the object.

Physics 201 – p. 10/31 Plane Mirrors

Physics 201 – p. 11/31 Plane Mirrors: Example

You are 1.70 m tall and your eyes are 0.10 m below the top of your head. You stand in front of a mirror and you want to see your full height, no more, no less. What is the minimum height of the mirror?

Physics 201 – p. 12/31 Plane Mirrors: Example

Physics 201 – p. 13/31 Plane Mirrors: Example

Let the light ray coming from your feet strike the bottom of the mirror and label that path by AB. See the figure drawn in class. Let BC be the reflected ray reaching the eye. The normal to the mirror from its bottom is denoted by BD. ABD and DBC are identical triangles. 1 1 AD = DC = 2AC = 2(1.70 − 0.10) = 0.80m Similarly, let the light ray from the top of the head reaching the top of the mirror be FE and the reflected ray reaching the eyes be EC. We 1 have 2CF = 0.05m.

Physics 201 – p. 13/31 Plane Mirrors: Example

The minimum height of the mirror is 1 d = FA − AD − 2CF = 1.70m − 0.80m − 0.05m = 0.85m Half of your height!

Physics 201 – p. 14/31 Spherical Mirrors

Physics 201 – p. 15/31 Spherical Mirrors

Spherical Mirrors: Mirrors whose shape is a segment of a sphere. Characterized by a principal axis which intersects with the “middle” of the mirror. On that axis, there is a point called center of curvature C situated at a distance R from the “middle” of the mirror. Concave Mirror: Spherical mirrors where parallel light rays from a distance source when shined on it are reﬂected at a single point: focal point F . The focal point is at f = R/2.

Physics 201 – p. 15/31 Spherical Mirrors

Convex mirror: Spherical mirror whose light rays which are incident on it diverge. Also called diverging mirror.

Physics 201 – p. 16/31 Spherical Mirrors

Physics 201 – p. 17/31 Spherical Mirrors

Physics 201 – p. 18/31 Spherical Mirrors

Physics 201 – p. 19/31 Spherical Mirrors

Physics 201 – p. 20/31 Spherical Mirrors

Physics 201 – p. 21/31 Spherical Mirrors

When light rays from an object are incident on such mirrors, how can one find the image? Is it real or virtual? Ray Diagrams for Mirrors: Ray 1 (F-ray) is drawn parallel to the principal axis and is reflected back through the focal point F . Ray 2 (P-ray) is drawn through the focal point. It is reflected back parallel to the principal axis. Ray 3 (C-ray) is drawn through the center of curvature C and is reflected back on itself. Physics 201 – p. 21/31 The intersection of any two of these rays Spherical Mirrors: Concave Mirror

Physics 201 – p. 22/31 Spherical Mirrors: Convex Mirror

Physics 201 – p. 23/31 Spherical Mirrors: Image from Conv

Physics 201 – p. 24/31 Spherical Mirrors

Important characteristics: For a convex mirror, the image is always virtual, upright and reduced in size.

Physics 201 – p. 25/31 Spherical Mirrors

Important characteristics: For a convex mirror, the image is always virtual, upright and reduced in size. For a concave mirror, it depends on where the object is located.

Physics 201 – p. 25/31 Spherical Mirrors

Beyond C ⇒ inverted, reduced in size, and real.

Physics 201 – p. 26/31 Spherical Mirrors

Beyond C ⇒ inverted, reduced in size, and real. At C ⇒ inverted, same as object, and real.

Physics 201 – p. 26/31 Spherical Mirrors

Beyond C ⇒ inverted, reduced in size, and real. At C ⇒ inverted, same as object, and real. Between C and F ⇒ inverted, enlarged, and real.

Physics 201 – p. 26/31 Spherical Mirrors

Beyond C ⇒ inverted, reduced in size, and real. At C ⇒ inverted, same as object, and real. Between C and F ⇒ inverted, enlarged, and real. Just beyond F ⇒ inverted, approaching inﬁnity, and real. Just inside F ⇒ upright, approaching inﬁnity, and virtual. Between F and the mirror ⇒ upright, enlarged, and virtual. Physics 201 – p. 26/31 Spherical Mirrors: Concave Mirror

Physics 201 – p. 27/31 Spherical Mirrors: Mirror Equation

Let the distance between the object and the mirror be p (d0 in the book) and the distance between the image and the mirror be q (di in the book). The magniﬁcation (ratio between sizes) is deﬁned by: ′ h −q − di M = h = p = d0

Physics 201 – p. 28/31 Spherical Mirrors: Mirror Equation

Physics 201 – p. 28/31 Spherical Mirrors: Concave Mirror

Physics 201 – p. 29/31 Spherical Mirrors: Sign Conventions

f < 0: Convex; f > 0: Concave

Physics 201 – p. 30/31 Spherical Mirrors: Sign Conventions

f < 0: Convex; f > 0: Concave m> 0: Upright image; m< 0: Inverted image

Physics 201 – p. 30/31 Spherical Mirrors: Sign Conventions

f < 0: Convex; f > 0: Concave m> 0: Upright image; m< 0: Inverted image

q > 0 (di > 0): Image (real) in front of mirror; q < 0 (di < 0): Image (virtual) behind mirror

Physics 201 – p. 30/31 Spherical Mirrors: Example

Physics 201 – p. 31/31 Spherical Mirrors: Example

A concave spherical mirror has a focal length of 10.0cm. Locate the images for object distances of (a) 25.0cm, (b) 10.0cm, (c) 5.00cm. 1 1 1 ⇒ 25.0cm + q = 10.0cm q = 16.7cm. −q −16.7cm − M = p = 25.0cm = 0.667 Smaller and inverted. 1 1 1 ⇒ 10.0cm + q = 10.0cm q = inﬁnity. 1 1 1 ⇒ − 5.0cm + q = 10.0cm q = 10.0cm. It is virtual since it is behind the mirror. −q −−10.0cm M = p = 5.0cm = 2 Upright and enlarged.

Physics 201 – p. 31/31