The Pinhole Camera

• Pinhole camera – A box with a pinhole in it and a screen opposite upon which an image forms.

• The information about the flame comes from the light from the flame that goes through the pin hole. This light falls on the bottom of the screen.
• Similarly, information about the bottom of the candle comes from the light from the bottom of the candle that goes through the pin hole. This light falls on the top of the screen.
• Because only light from the flame falls on the bottom of the screen, we see the image of the flame at the bottom. Similarly, since only light from the bottom of the candle falls on the top of the screen, we see the bottom of the candle there.
• Consider this pinhole camera and the associated calculations.

• The formation of the image is evidence that light travels in straight lines.
• From the above calculations, the equation for calculating image height and distance, and object height and distance as well as magnification is:

• M = magnification of the object (+ if the image is erect and – if the image is inverted).
• h_i = height of the image (- if inverted). h_o = the height of the object.
• d_i = distance to the image (always + for a pinhole camera.). d_o = the distance to the object (always + for pinhole camera).
• Real image – An image that can be formed on a screen, or an image through which the rays of light pass.
• Virtual image –An image that cannot be formed on a screen or an image through which the rays of light do not pass.
• Characteristics of the image are stated in terms of attitude (inverted or erect), size (in relation to object or magnification), and its type (real or virtual).

Plane Reflectors

• Opaque – light cannot travel through.
• Transparent –light can travel through
• Mirrors and brightly polished opaque surfaces reflect light. Reflection off of plane mirrors or reflectors obey the first and second laws of reflections.

• The equation for image height and distance developed above applies to plane mirrors. The image height will equal the object height and the image distance will equal to the object distance (i.e. The image will be the same height as the object and as far behind the mirror as the object is in front of the mirror).

Spherical Reflectors

• There are two types of spherical reflectors.
  • Concave – (converging mirror) reflected rays converge on each other.

• Convex – (diverging mirror) reflected rays diverge from each other.

• These two terms (concave and convex also apply to lenses. A concave lens causes refracted rays to diverge from each other. A convex lens causes refracted rays to converge on each other.

• Center of Curvature (C) – The centre of a spherical reflecting surface
• Radius of Curvature (R) – any straight line drawn from the centre of curvature to the curved surface
• Vertex (V) – The geometric centre of a curved mirror
• Principal Axis (PA) – The straight line passing through the vertex and centre of curvature
• Principal Focus (F) – The point on the principal axis where parallel rays reflect through.
  • The principle focus is half way between the center of curvature and the vertex.

• Focal Length (f) – The distance along the principal axis between the principal focus and the vertex.

• Spherical aberration – This is an effect that distorts the image produced by spherical reflectors.
  • Caused because some rays near the edge of a large converging mirror are not reflected to the principal focus.
• Spherical aberration can be corrected by
  • Making the width of the mirror smaller than the radius of curvature
  • Design a mirror with a parabolic shape.
• For diverging mirrors (convex), reflected rays diverge.
  • If extended backwards behind the mirror, these rays pass through a common point
• Virtual focus – The common point projected rays pass through for convex mirrors.
• Rays that are directed towards C (the center of curvature) are reflected back along the same path. This is true for convex or concave mirrors.

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November 19, 2013