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ray optics and optical instruments | ncert class 12
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notes and questions for ncert class 12 chapter 9 ray optics and optical instruments
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CHAPTER – 9RAY OPTICS AND OPTICAL INSTRUMENTS
Key points:-
• Principal focus of a concave & convex mirror
• Spherical Abberation
• Relation between focal length & radius of curvature
• Mirror formula
• Spherical mirrors – Concave & Convex , Applications , Linear magnification
• Refraction – Laws of refraction , refractive index , Applications
• Refraction through a glass slab
• Total internal reflection , Applications
• Curved surface formula
• Lens Makers formula & thin lens formula
• Linear magnification , power & combination of lenses
• Refraction through a prism , i- δ curve
• Dispersion
• Scattering , Ray Leigh’s scattering
• Optical instruments – Telescope & Microscope
DEFINITION OF BASIC TERMS
1.PRINCIPAL FOCUS OF A CONCAVE MIRROR : light rays which are coming parallel to the principal axis
after reflection converge to a point on the principal axis , called principal focus of concave mirror.
,2.PRINCIPAL FOCUS OF A CONVEX MIRROR : light rays which are coming parallel to the principal axis
after reflection from the convex mirror appears to diverge from a point on the principal axis, on the
other side of the mirror , called principal focus of convex mirror.
3.SPHERICAL ABBERATION : optical effect observed in an optical device (lens, mirror, etc.) that occurs
due to the increased refraction of light rays when they strike a lens or a reflection of light rays when
they strike a mirror near its edge, in comparison with those that strike nearer the centre.
Methods to minimize spherical ABBERATION:-
• by using stop for marginal rays so that only central rays are allowed to pass through .
• by using parabolic mirrors.
,RELATION BETWEEN FOCAL LENGTH (f) & RADIUS OF CURVATURE (R)
From the figure, A ray AB parallel to the principal axis is incident on a concave mirror . After reflection
the ray passes through ‘F’.
From ∆BCD,
tan θ = BD/CD ……..(1)
From ∆BFD ,
tan 2θ = BD/FD …….(2)
If θ is very small , tan θ ≈ θ & tan 2 θ ≈ 2 θ
Therefore , equations (1)&(2) becomes ,
Θ = BD/CD
2 θ = BD/FD
So , BD/FD = 2 × (BD/CD)
(1/FD) = 2/(CD) ……(3)
Here , FD = f & CD = R
Therefore ,
R = 2f
NEW CARTESIAN SIGN CONVENTION
1)All distances are measured from the pole of the mirror.
2) All distances measured in the direction of incident ray are taken as positive.
, 3) All distances measured against the direction of incident ray are taken as negative.
4) Heights measured perpendicular to the principal axis and upwards are taken as positive.
5) Heights measured perpendicular to the principal axis and downwards are taken as negative.
MIRROR FORMULA
Let a linear object be placed on the principal axis of a concave mirror . B is the image of AB .
Here , ∆A’B’F & ∆MPF are similar .
So , A’B’/MP = B’F/PF ……….(1)
Similarly , ∆A’B’P & ABP are similar
So , A’B’/AB = B’P/BP …………(2)
From equations (1)&(2) ,
B’F/PF = B’P/BP
(B’P – PF)/PF = B’P/BP …….(3)
By applying new Cartesian sign convention ,
B’P = –v
PF = –f
BP = –u
So equation (3) becomes ,
(–v+f)/(-f) = –v/–u = v/u
(v/f)–1 = v/u
Dividing with v ,
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