17'4 Thin lenses

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17.4 Thin lenses

• is defined as a transparent material with two
  spherical refracting surfaces whose thickness is
  thin compared to the radii of curvature of the
  two refracting surfaces.
• There are two types of thin lenses. It is
  converging and diverging lenses.
• Figures 1.18a and 1.18b show the various types of
  thin lenses, both converging and diverging.

(a) Converging (Convex) lenses
Biconvex
Plano-convex
Convex meniscus
Figure 1.18a
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(b) Diverging (Concave) lenses
Biconcave
Plano-concave
Concave meniscus
Figure 1.18b

• 17.4.1 Terms of thin lenses
• Figures 1.19 show the shape of converging
  (convex) and diverging (concave) lenses.

(a) Converging lens
(b) Diverging lens
Figure 1.19
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• Centre of curvature (point C1 and C2)
• is defined as the centre of the sphere of which
  the surface of the lens is a part.
• Radius of curvature (r1 and r2)
• is defined as the radius of the sphere of which
  the surface of the lens is a part.
• Principal (Optical) axis
• is defined as the line joining the two centres of
  curvature of a lens.
• Optical centre (point O)
• is defined as the point at which any rays
  entering the lens pass without deviation.

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17.4.2 Focal point and focal length, f

• Consider the ray diagrams for converging and
  diverging lenses as shown in Figures 1.20a and
  1.20b.
• From the figures,
• Points F1 and F2 represent the focus of the
  lenses.
• Distance f represents the focal length of the
  lenses.

Figure 1.20a
Figure 1.20b
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• Focus (point F1 and F2)
• For converging (convex) lens is defined as the
  point on the principal axis where rays which are
  parallel and close to the principal axis
  converges after passing through the lens.
• Its focus is real (principal).
• For diverging (concave) lens is defined as the
  point on the principal axis where rays which are
  parallel to the principal axis seem to diverge
  from after passing through the lens.
• Its focus is virtual.
• Focal length ( f )
• is defined as the distance between the focus F
  and the optical centre O of the lens.

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17.4.3 Ray diagram for thin lenses

• Figures 1.21a and 1.21b show the graphical method
  of locating an image formed by a converging
  (convex) and diverging (concave) lenses.

(a) Converging (convex) lens
Figure 1.21a
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(b) Diverging (concave) lens
Figure 1.21b

• Ray 1 - Parallel to the principal axis, after
  refraction by the lens, passes through the
  focal point (focus) F2 of a converging
  lens or appears to come from the focal point
  F2 of a diverging lens.
• Ray 2 - Passes through the optical centre of the
  lens is undeviated.
• Ray 3 - Passes through the focus F1 of a
  converging lens or appears to converge
  towards the focus F1 of a diverging lens,
  after refraction by the lens the ray parallel to
  the principal axis.

At least any two rays for drawing the ray
diagram.
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• Images formed by a diverging lens
• Figure 1.22 shows the graphical method of
  locating an image formed by a diverging lens.
• The characteristics of the image formed are
• virtual
• upright
• diminished (smaller than the object)
• formed in front of the lens.
• Object position ?? any position in front of the
  diverging lens.

Front
back
Figure 1.22
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• Images formed by a converging lens
• Table 1.5 shows the ray diagrams of locating an
  image formed by a converging lens for various
  object distance, u.

• Real
• Inverted
• Diminished
• Formed between point F2 and 2F2.
• (at the back of the lens)

u gt 2f
back
Front
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• Real
• Inverted
• Same size
• Formed at point 2F2. (at the back of the lens)

u 2f
Front
back

• Real
• Inverted
• Magnified
• Formed at a distance greater than 2f at the back
  of the lens.

f lt u lt 2f
Front
back
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• Real or virtual
• Formed at infinity.

u f
Front
back

• Virtual
• Upright
• Magnified
• Formed in front of the lens.

u lt f
back
Front
Table 1.5