PHYS 208 Lecture 25

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Geometric Optics (cont'd)

1. $n_{1}\sin {\theta _{1}}=n_{2}\sin {\theta _{2}}$
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 ($f$).

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:

${\frac {1}{s}}+{\frac {1}{s'}}={\frac {1}{f}}$

• Positive distance is object-side
• Negative distance is behind mirror surface
• Focal length for spherical mirror of radius $R$ is $R/2$

For an object that has a height of $h$, its image height will be determined by the magnification ($M$):

$M={\frac {h'}{h}}=-{\frac {s'}{s}}$

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 $f$ 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,

${\frac {1}{s}}+{\frac {1}{s'}}={\frac {1}{f}}$ $M={\frac {h'}{h}}=-{\frac {s'}{s}}$

Positive magnification is upright, negative is inverted

Lens Maker's Formula

${\frac {1}{f}}=(n-1)\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right)$

Where

• $n$ is the index of refraction of the lens material
• $R_{1}$ is the radius of the curvature of face 1
• $R_{2}$ 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.