Chapter : 9

What are Ray Optics and Optical Instruments ?

Topic

Apparent Depth

Formula

Apparent depth
= (real dept/µ)

Symbol Representation

µ=refractive index

=(sin i/sin r)(Snell's law)

i = incident angle of ray

r = angle of refraction

Important Points

When we look into a pool of water,
the bottom of the pool will appear to be raised due to refraction of light.

Critical Angle

c = sin-1(1/µ) or μ = (1/sin c)

μ = refractive index of denser medium w.r.t. rarer medium

c = critical angle which depends on colour of light

Phenomenon of refraction of light
into denser medium from the boundary of denser medium with rarer medium known as total internal reflections

i>ic

Some of the important applications
of total internal reflection:

(a) Diamond brilliance

(b) Optical fiber

(c) Mirage

Lens Maker’s
Formula

(1/f)=(µ-1) ( (1/R1)-(1/R2))

μ = refractive index of material of lens w.r.t. medium in which lens is placed.

R1, R2 = radii of curvature of the two surfaces of the lens.

This formula is valid for all
types of lenses.

Thin Lens
Formula

(1/v)-(1/u) =( 1/f)

u = distance of the object from the optical centre of the lens

v = distance of image from the optical centre of the lens

f = focal length of the lens

f is positive for converging or convex lens and negative for diverging or concave lens.

Linear Magnification

m=(I/O)-(V/U)

v = size of image

u = size of object

m is positive for virtual image and m is negative for real image.

Topic Formula Symbol Representation Important Points
Power of a Lens P = (1/f) f = focal length in metres Unit of power of lens
= dioptre
= 1D
= 1m-1
• Ability of lens to converge or diverge a beam of light.
• P is positive for a convex lens and negative for a concave lens.
• When focal length of a lens is in cm, then P =(100/f(in cm))dioptre
Combination of then lenses •(1/F1)+(1/F2)+(1/F)
• P = P1 + P2
• m = m1 × m2
F1, F2 = Focal length of two thin lenses places coaxially
F = focal length of combination
P = Power of lens with proper sign
m1, m2 = magnification
Combination of lens used for:
• Increase the magnification of image
• Make the final image erract w.r.t. object
• Reduce certain observations
Angle of deviation δ = i1 + i2 – A i1 = angle of incidence
i2 = angle of emergence
A = r1 + r2 = angle of prism
The difference between the sum of incident angles and the sum of emergent angles is known as the angle of deviation.
Prism Formula μ = sin[(A+δm)/2]/sin(A/2)
(Snell’s law)
A = angle of prism
δm= angle of minimum deviation
i = angle of incidence
δm = 2 i – A
when i1 = i2
and r1 = r2
• For thin prism,
Sin [A+δm]/2→(A+δm/2) and Sin (A/2)→(A/2)
• δ = (μ–1)A this is the formula of angle of maximum deviation.
Angular Dispersion θ = δV – δR
= (µV – μR) A
δV, δR = Deviation of violet and red light
μV, μR = Refractive index for violet and Red colour.
The difference in the angle of deviation between two extreme colours is known as angle of dispersion or angular dispersion for the two colours.
Magnifying Power of Simple Microsope • Image, at the least distance of vision m=1+(D/f)
• Image at infinity m=(D/f)
m = magnification
D = least distance vision
A simple microscope or a simple magnifying glass is a converging lens of small focal length.
Magnifying Power of Compound Microscope • Image, at infinity
m=(-L/v0(D/fe))
• Image, at the least distance of vision
m =(-Vo/Uo(1+(D/fe))
uo = distance of object from the objective lens
vo=L=distance of image from the objective lens (length of microscope tube)
fe = focal length of the eye lens
D = least distace of distinct vision.
• Compound microscope is the combination of two convex lenses one compounding the effect of the other, for much larger magnification.
• The objective have smaller aperture and smaller focal length than the eye-piece.
Topic Formula Symbol Representation Important Points
Mirror Formula (1/u)+(1/v)=(1/f) u = distance of object from the pole of the mirror
v = distance of image
f = (R/2)
• Mirror formula is same for both concave and convex mirrors equation remain uneffected whether the image is real or virtual.
Linear Magnification • m =(size of image (h2)/size of object (h1))
• m =(f/f-v)
f = focal length of magnifying lens. In case of concave mirror, when image is real,
m = negative.
When image is virtual, m is positive.
Use of spherical mirror • As reflector in street lamps, search light.
• Driving mirror
• Telescopes, solar cookers
Optical fiber • Based on total internal reflection.
• Use for data transmission using light pulses.
• Made of plastic or glass.
Magnifying Power Astronomical Telescope (Refracting Type) • When the final image is formed at infinity (Normal Adjustment),
m=(fo/fe)
• When the final image is formed at least distance of distinct vision,
m =(-fo/fe)(1+(fe/D))
fo = Focal length of objective lens
fe = Focal length of the eye-piece
D = least distance of distinct vision (i.e. 25 cm)
• Astronomic telescope (Refracting type) is consist of two converging lense the objective lens has large focal length and large aperture than the eye-piece.
Magnifying Power of Reflecting Type Telescope In normal adjustment
m =(-fo/fe)=((R/2)/fe)
R = radius of curvature of concave mirror • It is improvement over refracting type telescope. Here, the objective lens is replaced by a concave parabolic mirror.