PHYS 208 Lecture 25

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Geometric Optics (cont'd)

1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_1\sin{\theta_1} = n_2\sin{\theta_2}}
2. angle of incidence = angle of reflection

Mirrors and Reflection

In spherical concave mirror, there is a point at which all incoming rays intersect (focal point). The distance from the surface to this point is called the focal length (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} ).

In a spherical convex mirror, there is also a focal point, but it is the point from which all reflected (parallel) rays seem to originate, and it is within/behind the surface (thus a virtual image)

For both cases, there is a distance from object to surface, from surface to image, and the focal length:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{s} + \frac{1}{s'} = \frac{1}{f}}

• Positive distance is object-side
• Negative distance is behind mirror surface
• Focal length for spherical mirror of radius Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R/2}

For an object that has a height of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h} , its image height will be determined by the magnification (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} ):

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M = \frac{h'}{h} = -\frac{s'}{s}}

Positive magnification is upright, negative is inverted

Lenses and Refraction

Convex Lenses (counterpart to concave mirrors in that focal length is positive)

• double-convex () (intersection of two spheres as in a venn diagram)
• planoconvex (| (sphere chopped off at plane)
• convex meniscus (( (sphere cut off at another spherical surface as in a contact lens)

Concave Lenses (counterpart to convex mirrors in that focal length is negative)

• double-concave )(
• planoconcave )|
• concave meniscus ))

Distance from center of lens to focal point is focal length. The plane parallel to the lens plane and at a distance of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is the focal plane

Positive distance is on opposite side of lens from object (real image) Negative distance is on object side of lens (virtual image)

For a convex lens, parallel lines must be refracted through the focal point; lines that pass through the center of the lens are undeflected. Their intersection is at a corresponding point on the image.

Just like in mirror equations,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{s} + \frac{1}{s'} = \frac{1}{f}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M = \frac{h'}{h} = -\frac{s'}{s}}

Positive magnification is upright, negative is inverted

Lens Maker's Formula

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)}

Where

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the index of refraction of the lens material
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_1} is the radius of the curvature of face 1
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_2} is the radius of curvature of face 2

Interference

Light is reflected by the top and bottom surfaces of a thin film due to phase changes.

Our eye percieves both sources simultaneously... more on this next time.