1 Thin Lens Light refracts on the interface of two media, following Snell’s law of refraction: Light bends through a triangular prism: θ 1 and θ 2 are both with respect to the normal o f the interface. The parameters n 1 and n 2 are call the index of m edium 1 and 2 respectiv ely. 2 2 1 1 sin in n s n Medium 1 Medium 2 θ 1 θ 2 Light converges
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1 Thin Lens Light refracts on the interface of two media, following Snell’s law of refraction: Light bends through a triangular prism: θ 1 and θ 2 are.
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1
Thin Lens
Light refracts on the interface of two media, following Snell’s law of refraction:
Light bends through a triangular prism:
θ1 and θ2 are both with respect to the normal of the interface.The parameters n1 and n2 are call the index of medium 1 and 2 respectively.
2211 sinin nsn Medium 1
Medium 2
θ1
θ2
Light converges
2
Thin Lens
Light bends through an upside-down triangular prism:
Light diverges
The back traces of the diverging light meet at one point.
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Thin lens
Converging thin lens: All light rays parallel to the principal axis meet at the focal point on the
other side of the lens (far focal point). The focal points on either side of the lens are equal distance from the
center of the lens. This distance is called the focal length and it is a positive value.
It is considered that the thin lens has no thickness. And it is of represented by a double out-going arrowed line.
Converging thin lens
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Thin lenses
Diverging thin lens: All light rays parallel to the principal axis diverge, but their back traces
meet at the focal point on the same side of the lens (near focal point). The focal points on either side of the lens are equal distance from the
center of the lens. This distance is called the focal length and is a negative value.
It is considered that the thin lens has no thickness. And it is of represented by a double inward-going arrowed line.
Diverging thin lens
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Find image with a thin lens
Converging lens
Ray 1:Parallel to axis, then passes through far focal point
Ray 2:Passes unchanged through center of lens
Ray 3:Passes through near focal point, then parallel to axis
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Find image with a thin lens
Converging lens
F
F
fObject
hodo
Real image, inverted, smaller
hi
di
o
i
o
i
d
d
h
hm :ionmagnificat
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Find image with a thin lens
Converging lens
FF
f2f
Real, inverted, smaller
FF
f2f
Real, inverted, same size
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Find image with a thin lens
Converging lens
FF
f2f
Real, inverted, larger
FF
f2f No image
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Find image with a thin lens
Converging lens
FF
f2f
Virtual, upright,larger
Like in the converging mirror case, there are 5 possible object locations that produce different images.
Diverging lens,Like in the diverging mirror case, no matter where the object is placed, you always get a virtual, upright and smaller image.
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Find image with a thin lens
Diverging lens
Ray 1Parallel to axis, virtual ray passes through near focal point
Ray 2Straight through center of lens
Ray 3Virtual ray through far focal point, virtual ray parallel to axis
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Find image with a thin lens
Diverging lens
F
Ff
Object
hodo
Virtual image, upright, smaller
hi
di
o
i
o
i
d
d
h
hm :ionmagnificat
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Analytical calculations
Thin lens equation.
fdd oi
111
o
i
o
i
d
d
h
hm :ionmagnificat
ho
hi
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Analytical calculations
In the mirror case, there is a formula connects the radius and focal length:
Here the value of the radius is always positive.
2
Rf
2
Rf
Converging mirror Diverging mirror
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Analytical calculations
Lens maker’s equation:
The formula for a lens in vacuum (air):
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111
1
RR)n(
f
n : index of refraction of the lens material.R1 : radius of near surface. R2 : radius of far surface. The near or far surface is with respect to the focal point F. Near
side is surface 1, far side is surface 2. The sign of the radius is then defined as
“+” if the center is on the far side; “-” if the center is on the near side. In this convention, positive f means converging lens, negative f means diverging lens.
F
near surface
far surface
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Analytical calculations
Lens maker’s equation:
The formula for a lens (nlens) in medium nmedium :
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111
1
RR)
n
n(
f medium
lensR1 : radius of near surface. R2 : radius of far surface.
F
near surface
far surface
nmedium
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More sign conventions
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Sign convention table
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Example 1
Find the image distance.
/m di = 1.0 m
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Example 2
Prove for a thin lens, the focal length on both side of the lens is the same.
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Example 3
A thin lens has a focal lens of fa = 5 mm in air. The index of refraction of the lens material is 1.53. If this lens is placed in water (n = 1.33), what will the lens’ focal length in water?
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Example 4
A thin lens has a near surface with a radius of curvature of −5.00 cm and a far surface with a radius of curvature of +7.00 cm. (a) Is the lens converging or diverging? (b) What is the focal length of the lens if the index of refraction of the material is 1.74?
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Example 5
A small light bulb is placed a distance d from a screen. You have a converging lens with a focal length of f. There are two possible distances from the bulb at which you could place the lens to create a sharp image on the screen. (a) Derive an equation for the distance z between the two positions that includes only d and f. (b) Use this equation to show that the distance d between an object and a real image formed by a converging lens must always be greater than or equal to four times the focal length f.