Lecture 23: Thin Lenses

23.7, 23.8, 23.10

What are thin lenses

those whose thickness is small compared to their radius of curvature

types of thin lenses

converging or diverging

light rays parallel to the principle axis are brought to … by a … lens

• a focus

• converging

no matter whether the right rays are parallel to the principle axis or not

• they will always focus on a line through the focal point

• line is called the focal plane

diverging lens make … light diverge

• parallel

the focal point is that point where the diverging rays would converge if projected back

refractive power of a lens is the inverse of

its focal length in metres

refractive power is measured in diopters (D), this unit is used in optometry

P = 1/f(m)

eg) what is the power of a lens whose f = 50 cm

P = 1/f(m) → 1/0.5 = 2 D

Lens equation

• same as the mirror equation but sign convention is different

• 1/do + 1/di = 1/f

• magnification = m = hi/ho = -di/do

SIGN CONVENTION

• +f = convex

• -f = concave

SPHERICAL MIRRORS

• -f = convex

• +f = concave

1.7 m tall person is standing 2.5 m in front of a camera of f = 0.05 m, fine the image distance, magnification and image height

1/do + 1/di = 1/f

1/2.5 + 1/di = 1/0.05

di = 0.051 m → real since positive

m = hi/ho = -di/do = - 0.051/2.5 = -0.02 → image is inverted as magnification is negative

hi = (-0.02)x1.7 = -0.035 m

virtual image is always

upright

real image is always

inverted

convex lens makes…

• real image when do > f

• virtual image when do < f

concave lens always makes…

virtual image no matter where the object is located

lens makers’ equation

• this equation relates the radii of curvature of the two lens surfaces and the index of refraction to the focal length of the lens

The glass lenses shown below has R1 = R2 = 42 cm and n = 1.65
Find their focal length

converging lens

• 1/f = (n-1)(1/R1 + 1/R2)

• 1/f = (1.65 -1)(1/42 + 1/42)

• f = +32 cm

diverging lens

• 1/f = (1.65 -1)(1/-42 + 1/-42)

• f = -32 cm